2000 character limit reached
Application of Deep Learning Reduced-Order Modeling for Single-Phase Flow in Faulted Porous Media (2403.03678v1)
Published 6 Mar 2024 in math.NA and cs.NA
Abstract: We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach benefits from a mixed-dimensional framework that effectively manages the resulting non-conforming mesh. To streamline complex and repetitive calculations such as sensitivity analysis and solution of inverse problems, we utilize the Deep Learning Reduced Order Model (DL-ROM). This non-intrusive neural network-based technique is evaluated against the traditional Proper Orthogonal Decomposition (POD) method across various scenarios, demonstrating DL-ROM's capacity to expedite complex analyses with promising accuracy and efficiency.
- C. Lu, Y. Sun, T.A. Buscheck, Y. Hao, J.A. White, L. Chiaramonte, Uncertainty quantification of CO2𝐶subscript𝑂2CO_{2}italic_C italic_O start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT leakage through a fault with multiphase and nonisothermal effects. Greenhouse Gases: Science and Technology 2(6), 445–459 (2012). 10.1002/ghg.1309 [3] A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-15431-2 [4] J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-15431-2 [4] J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Greenhouse Gases: Science and Technology 2(6), 445–459 (2012). 10.1002/ghg.1309 [3] A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-15431-2 [4] J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-15431-2 [4] J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.1007/978-3-319-15431-2 [4] J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations (Springer International Publishing, 2016). 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.1007/978-3-319-22470-1 [5] S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S.L. Brunton, J.N. Kutz, Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control (Cambridge University Press, 2019), p. 492. 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.1017/9781108380690 [6] P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, V.L. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, 2005), p. 395 [7] Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Y. Maday, , N.C. Nguyen, A.T. Patera, S.H. Pau, , and, A general multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Communications on Pure and Applied Analysis 8(1), 383–404 (2009). 10.3934/cpaa.2009.8.383 [8] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- P.J. Schmid, Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics 656, 5–28 (2010). 10.1017/s0022112010001217 [9] A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Kalur, P. Mortimer, J. Sirohi, R. Geelen, K.E. Willcox, Data-driven closures for the dynamic mode decomposition using quadratic manifolds, in AIAA AVIATION 2023 Forum (American Institute of Aeronautics and Astronautics, 2023). 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.2514/6.2023-4352 [10] B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, M. Gunzburger, Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- SIAM Review 60(3), 550–591 (2018). 10.1137/16m1082469 [11] B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models. Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Computer Methods in Applied Mechanics and Engineering 291, 21–41 (2015). 10.1016/j.cma.2015.03.018 [12] F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F.J. Gonzalez, M. Balajewicz, Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems. arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- arXiv:1808.01346 (2018). 10.48550/ARXIV.1808.01346 [13] T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 T. Murata, K. Fukami, K. Fukagata, Nonlinear mode decomposition with convolutional neural networks for fluid dynamics. Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Journal of Fluid Mechanics 882 (2019). 10.1017/jfm.2019.822 [14] K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Theoretical and Computational Fluid Dynamics 34(4), 367–383 (2020). 10.1007/s00162-020-00528-w [15] S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, L. Dede’, A. Manzoni, A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Journal of Scientific Computing 87(2) (2021). 10.1007/s10915-021-01462-7 [16] S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Fluids 6(7), 259 (2021). 10.3390/fluids6070259 [17] S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Computer Methods in Applied Mechanics and Engineering 388, 114181 (2022). 10.1016/j.cma.2021.114181 [18] S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Fresca, F. Fatone, A. Manzoni, Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Mathematics in Engineering 5(6), 1–36 (2023). 10.3934/mine.2023096 [19] N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N. Franco, A. Manzoni, P. Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations. Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Mathematics of Computation 92(340), 483–524 (2022). 10.1090/mcom/3781 [20] N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 N.R. Franco, S. Fresca, A. Manzoni, P. Zunino, Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Neural Networks 161, 129–141 (2023). 10.1016/j.neunet.2023.01.029 [21] F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni. Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Latent dynamics networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes (2023). 10.48550/ARXIV.2305.00094 [22] M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Wangen, Physical principles of sedimentary basin analysis (Cambridge University Press, 2009) [23] D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- D. Boffi, F. Brezzi, M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2013) [24] V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 V. Martin, J. Jaffré, J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- SIAM Journal on Scientific Computing 26(5), 1667–1691 (2005). 10.1137/s1064827503429363 [25] C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. D’Angelo, A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Mathematical Modelling and Numerical Analysis 46(02), 465–489 (2012). 10.1051/m2an/2011148 [26] B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media. Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Advances in Water Resources 111, 239–258 (2018). 10.1016/j.advwatres.2017.10.036 [27] W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- SIAM Journal on Numerical Analysis 56(4), 2203–2233 (2018). 10.1137/17m1139102 [28] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Advances in Water Resources 147 (2020). 10.1016/j.advwatres.2020.103759 [math.NA] [29] L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 L. Formaggia, Handbook of Grid Generation (CRC Press, 1998), chap. Data Structures for Unstructured Mesh Generation [30] J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- J.M. Nordbotten, W.M. Boon, A. Fumagalli, E. Keilegavlen, Unified approach to discretization of flow in fractured porous media. Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Computational Geosciences 23(2), 225–237 (2018). 10.1007/s10596-018-9778-9 [31] J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Blazek, 3rd edn. (Butterworth-Heinemann, Oxford, 2015). https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- https://doi.org/10.1016/B978-0-08-099995-1.09986-3 [32] C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Hirish, Numerical Computation of Internal and External Flows (Elsevier, 2007). 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.1016/b978-0-7506-6594-0.x5037-1 [33] I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6(3), 405–432 (2002). 10.1023/a:1021291114475 [34] J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J.M. Nordbotten, E. Keilegavlen, in Polyhedral Methods in Geosciences (Springer International Publishing, 2021), pp. 119–158. 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.1007/978-3-030-69363-3_4 [35] M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 M. Starnoni, I. Berre, E. Keilegavlen, J.M. Nordbotten, Consistent MPFA discretization for flow in the presence of gravity. Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Water Resources Research 55(12), 10105–10118 (2019). 10.1029/2019wr025384 [36] I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Stefansson, I. Berre, E. Keilegavlen, Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Transport in Porous Media 124(2), 439–462 (2018). 10.1007/s11242-018-1077-3 [37] E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Keilegavlen, R. Berge, A. Fumagalli, M. Starnoni, I. Stefansson, J. Varela, I. Berre, Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- arXiv:1908.09869 (2019). 10.48550/ARXIV.1908.09869 [38] P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- SIAM Review 57(4), 483–531 (2015). 10.1137/130932715 [39] C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 C. Eckart, G. Young, The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Psychometrika 1(3), 211–218 (1936). 10.1007/bf02288367 [40] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen. Mathematische Annalen 63(4), 433–476 (1907). 10.1007/bf01449770 [41] R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R.A. DeVore, R. Howard, C. Micchelli, Optimal nonlinear approximation. Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Manuscripta Mathematica 63(4), 469–478 (1989). 10.1007/bf01171759 [42] A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation. Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Computers & Structures 85(11), 784–795 (2007). 10.1016/j.compstruc.2007.01.013 [43] D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D. Forti, G. Rozza, Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- International Journal of Computational Fluid Dynamics 28(3-4), 158–169 (2014). 10.1080/10618562.2014.932352 [44] S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 S. Aubert, F. Mastrippolito, Q. Rendu, M. Buisson, F. Ducros, Planar slip condition for mesh morphing using radial basis functions. Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Procedia Engineering 203, 349–361 (2017). 10.1016/j.proeng.2017.09.819 [45] D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.P. Kingma, J. Ba, Adam: A method for stochastic optimization. arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- arXiv:1412.6980 (2014). 10.48550/ARXIV.1412.6980 [46] I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 I. Berre, W.M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, A. Tatomir, K. Brenner, S. Burbulla, P. Devloo, O. Duran, M. Favino, J. Hennicker, I.H. Lee, K. Lipnikov, R. Masson, K. Mosthaf, M.G.C. Nestola, C.F. Ni, K. Nikitin, P. Schädle, D. Svyatskiy, R. Yanbarisov, P. Zulian, Verification benchmarks for single-phase flow in three-dimensional fractured porous media. Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Advances in Water Resources 147, 103759 (2021). 10.1016/j.advwatres.2020.103759 [47] J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 J. Feinberg, H.P. Langtangen, Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Journal of Computational Science 11, 46–57 (2015). 10.1016/j.jocs.2015.08.008 [48] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice (Wiley, 2004), p. 232 [49] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 1992). 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- 10.1002/9780470316849 [50] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Journal of Global Optimization 11(4), 341–359 (1997). 10.1023/a:1008202821328 [51] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2 P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y.V.B. and, SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2
- Nature Methods 17(3), 261–272 (2020). 10.1038/s41592-019-0686-2