Papers
Topics
Authors
Recent
Search
2000 character limit reached

AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification

Published 29 Sep 2023 in q-bio.QM, cs.AI, and cs.LG | (2310.01433v1)

Abstract: Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model, and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. While the current work focuses on the performance of AI-Aristotle based on synthetic data, it can equally handle noisy experimental data and can even be used for black-box identification in just a few minutes on a laptop. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (42)
  1. S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proceedings of the national academy of sciences, vol. 113, no. 15, pp. 3932–3937, 2016.
  2. R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 58, no. 1, pp. 267–288, 1996.
  3. D. L. Donoho, “Compressed sensing,” IEEE Transactions on information theory, vol. 52, no. 4, pp. 1289–1306, 2006.
  4. S.-M. Udrescu and M. Tegmark, “Ai feynman: A physics-inspired method for symbolic regression,” Science Advances, vol. 6, no. 16, p. eaay2631, 2020.
  5. C. Cornelio, S. Dash, V. Austel, T. R. Josephson, J. Goncalves, K. L. Clarkson, N. Megiddo, B. El Khadir, and L. Horesh, “Combining data and theory for derivable scientific discovery with ai-descartes,” Nature Communications, vol. 14, no. 1, p. 1777, 2023.
  6. I. Douven, The art of abduction. MIT press, 2022.
  7. K. R. Broløs, M. V. Machado, C. Cave, J. Kasak, V. Stentoft-Hansen, V. G. Batanero, T. Jelen, and C. Wilstrup, “An approach to symbolic regression using feyn,” arXiv preprint arXiv:2104.05417, 2021.
  8. C. Wilstrup and J. Kasak, “Symbolic regression outperforms other models for small data sets,” arXiv preprint arXiv:2103.15147, 2021.
  9. N. J. Christensen, S. Demharter, M. Machado, L. Pedersen, M. Salvatore, V. Stentoft-Hansen, and M. T. Iglesias, “Identifying interactions in omics data for clinical biomarker discovery using symbolic regression,” Bioinformatics, vol. 38, no. 15, pp. 3749–3758, 2022.
  10. M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational physics, vol. 378, pp. 686–707, 2019.
  11. A. D. Jagtap and G. E. Karniadakis, “Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations.,” in AAAI spring symposium: MLPS, vol. 10, 2021.
  12. E. Kiyani, K. Shukla, G. E. Karniadakis, and M. Karttunen, “A framework based on symbolic regression coupled with extended physics-informed neural networks for gray-box learning of equations of motion from data,” arXiv preprint arXiv:2305.10706, 2023.
  13. P. Andras, “Random projection neural network approximation,” in 2018 International Joint Conference on Neural Networks (IJCNN), pp. 1–8, IEEE, 2018.
  14. F. O. de Franca and M. Z. de Lima, “Interaction-transformation symbolic regression with extreme learning machine,” Neurocomputing, vol. 423, pp. 609–619, 2021.
  15. F. O. de França, “A greedy search tree heuristic for symbolic regression,” Information Sciences, vol. 442, pp. 18–32, 2018.
  16. B. E. Köktürk-Güzel and S. Beyhan, “Symbolic regression based extreme learning machine models for system identification,” Neural Processing Letters, vol. 53, no. 2, pp. 1565–1578, 2021.
  17. R. Rico-Martinez, J. Anderson, and I. Kevrekidis, “Continuous-time nonlinear signal processing: a neural network based approach for gray box identification,” in Proceedings of IEEE Workshop on Neural Networks for Signal Processing, pp. 596–605, IEEE, 1994.
  18. F. P. Kemeth, S. Alonso, B. Echebarria, T. Moldenhawer, C. Beta, and I. G. Kevrekidis, “Black and gray box learning of amplitude equations: Application to phase field systems,” Physical Review E, vol. 107, no. 2, p. 025305, 2023.
  19. R. J. Lovelett, J. L. Avalos, and I. G. Kevrekidis, “Partial observations and conservation laws: Gray-box modeling in biotechnology and optogenetics,” Industrial & Engineering Chemistry Research, vol. 59, no. 6, pp. 2611–2620, 2019.
  20. M. Quach, N. Brunel, and F. d’Alché Buc, “Estimating parameters and hidden variables in non-linear state-space models based on odes for biological networks inference,” Bioinformatics, vol. 23, no. 23, pp. 3209–3216, 2007.
  21. J. Wandy, M. Niu, D. Giurghita, R. Daly, S. Rogers, and D. Husmeier, “Shinykgode: an interactive application for ode parameter inference using gradient matching,” Bioinformatics, vol. 34, no. 13, pp. 2314–2315, 2018.
  22. C. Loos, S. Krause, and J. Hasenauer, “Hierarchical optimization for the efficient parametrization of ode models,” Bioinformatics, vol. 34, no. 24, pp. 4266–4273, 2018.
  23. A. Yazdani, L. Lu, M. Raissi, and G. E. Karniadakis, “Systems biology informed deep learning for inferring parameters and hidden dynamics,” PLoS computational biology, vol. 16, no. 11, p. e1007575, 2020.
  24. M. Daneker, Z. Zhang, G. E. Karniadakis, and L. Lu, “Systems biology: Identifiability analysis and parameter identification via systems-biology-informed neural networks,” in Computational Modeling of Signaling Networks, pp. 87–105, Springer, 2023.
  25. E. Schiassi, R. Furfaro, C. Leake, M. De Florio, H. Johnston, and D. Mortari, “Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations,” Neurocomputing, vol. 457, pp. 334–356, 2021.
  26. M. De Florio, E. Schiassi, and R. Furfaro, “Physics-informed neural networks and functional interpolation for stiff chemical kinetics,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32, no. 6, 2022.
  27. M. Virgolin and S. P. Pissis, “Symbolic regression is np-hard,” arXiv preprint arXiv:2207.01018, 2022.
  28. M. Cranmer, “Interpretable machine learning for science with pysr and symbolicregression. jl,” arXiv preprint arXiv:2305.01582, 2023.
  29. T. Stephens, “gplearn: Genetic programming in python, with a scikitlearn inspired api. [online]. available: https://github.com/trevorstephens/gplearn,” 2015.
  30. CRC Press, 2011.
  31. J. Sturis, K. S. Polonsky, E. Mosekilde, and E. Van Cauter, “Computer model for mechanisms underlying ultradian oscillations of insulin and glucose,” American Journal of Physiology-Endocrinology And Metabolism, vol. 260, no. 5, pp. E801–E809, 1991.
  32. D. J. Albers, N. Elhadad, E. Tabak, A. Perotte, and G. Hripcsak, “Dynamical phenotyping: using temporal analysis of clinically collected physiologic data to stratify populations,” PloS one, vol. 9, no. 6, p. e96443, 2014.
  33. D. Mortari, “The theory of connections: Connecting points,” Mathematics, vol. 5, no. 4, p. 57, 2017.
  34. M. De Florio, E. Schiassi, A. D’Ambrosio, D. Mortari, and R. Furfaro, “Theory of functional connections applied to linear odes subject to integral constraints and linear ordinary integro-differential equations,” Mathematical and Computational Applications, vol. 26, no. 3, p. 65, 2021.
  35. D. Mortari, “Least-squares solution of linear differential equations,” Mathematics, vol. 5, no. 4, p. 48, 2017.
  36. G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: theory and applications,” Neurocomputing, vol. 70, no. 1-3, pp. 489–501, 2006.
  37. E. Schiassi, M. De Florio, B. D. Ganapol, P. Picca, and R. Furfaro, “Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics,” Annals of Nuclear Energy, vol. 167, p. 108833, 2022.
  38. Z. Xiang, W. Peng, X. Liu, and W. Yao, “Self-adaptive loss balanced physics-informed neural networks,” Neurocomputing (Amsterdam), vol. 496, pp. 11–34, 2022. Peer Reviewed.
  39. L. D. McClenny and U. M. Braga-Neto, “Self-adaptive physics-informed neural networks,” Journal of Computational Physics, vol. 474, 2023.
  40. D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014.
  41. D. C. Liu and J. Nocedal, “On the limited memory bfgs method for large scale optimization,” Mathematical programming, vol. 45, pp. 503–528, Aug 1989.
  42. A. D. Jagtap, Y. Shin, K. Kawaguchi, and G. E. Karniadakis, “Deep kronecker neural networks: A general framework for neural networks with adaptive activation functions,” Neurocomputing, vol. 468, pp. 165–180, 2022.
Citations (21)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up