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Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI) (2310.04227v2)

Published 6 Oct 2023 in eess.SY and cs.SY

Abstract: Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.

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References (36)
  1. John Wiley & Sons, 2013.
  2. 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.
  3. B. Ho and R. E. Kálmán, “Effective construction of linear state-variable models from input/output functions: Die konstruktion von linearen modeilen in der darstellung durch zustandsvariable aus den beziehungen für ein-und ausgangsgrößen,” at-Automatisierungstechnik, vol. 14, no. 1-12, pp. 545–548, 1966.
  4. P. J. Schmid, “Dynamic mode decomposition of numerical and experimental data,” Journal of fluid mechanics, vol. 656, pp. 5–28, 2010.
  5. R. Babuška and H. B. Verbruggen, “An overview of fuzzy modeling for control,” Control Engineering Practice, vol. 4, no. 11, pp. 1593–1606, 1996.
  6. G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nature Reviews Physics, vol. 3, no. 6, pp. 422–440, 2021.
  7. P. J. Baddoo, B. Herrmann, B. J. McKeon, J. Nathan Kutz, and S. L. Brunton, “Physics-informed dynamic mode decomposition,” Proceedings of the Royal Society A, vol. 479, no. 2271, p. 20220576, 2023.
  8. M. Mattheakis, P. Protopapas, D. Sondak, M. Di Giovanni, and E. Kaxiras, “Physical symmetries embedded in neural networks,” arXiv preprint arXiv:1904.08991, 2019.
  9. M. Atwya and G. Panoutsos, “Structure optimization of prior-knowledge-guided neural networks,” Neurocomputing, vol. 491, pp. 464–488, 2022.
  10. J. J. Pannell, S. E. Rigby, and G. Panoutsos, “Physics-informed regularisation procedure in neural networks: An application in blast protection engineering,” International Journal of Protective Structures, vol. 13, no. 3, pp. 555–578, 2022.
  11. S. E. Otto, N. Zolman, J. N. Kutz, and S. L. Brunton, “A unified framework to enforce, discover, and promote symmetry in machine learning,” 2023.
  12. J. L. Pitarch, A. Sala, and C. de Prada, “A systematic grey-box modeling methodology via data reconciliation and SOS constrained regression,” Processes, vol. 7, no. 3, p. 170, 2019.
  13. A. A. Ahmadi and B. E. Khadir, “Learning dynamical systems with side information,” SIAM Review, vol. 65, no. 1, pp. 183–223, 2023.
  14. M. Khosravi and R. S. Smith, “Nonlinear system identification with prior knowledge on the region of attraction,” IEEE Control Systems Letters, vol. 5, no. 3, pp. 1091–1096, 2021.
  15. M. Khosravi and R. S. Smith, “Kernel-based identification with frequency domain side-information,” Automatica, vol. 150, p. 110813, 2023.
  16. A. Luppi, A. Bisoffi, C. D. Persis, and P. Tesi, “Data-driven design of safe control for polynomial systems,” European Journal of Control, p. 100914, 2023.
  17. R. Rodriguez, O. Ahmadzadeh, Y. Wang, and D. Soudbakhsh, “Discovering governing equations of li-ion batteries pertaining state of charge using input-output data,” in 2023 American Control Conference (ACC), pp. 3081–3086, IEEE, 2023.
  18. O. Ahmadzadeh, R. Rodriguez, Y. Wang, and D. Soudbakhsh, “A physics-inspired machine learning nonlinear model of li-ion batteries,” in 2023 American Control Conference (ACC), pp. 3087–3092, IEEE, 2023.
  19. M. Hoffmann, C. Fröhner, and F. Noé, “Reactive SINDy: Discovering governing reactions from concentration data,” The Journal of chemical physics, vol. 150, no. 2, 2019.
  20. S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Data-driven discovery of partial differential equations,” Science advances, vol. 3, no. 4, p. e1602614, 2017.
  21. S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Sparse identification of nonlinear dynamics with control (SINDYc),” IFAC-PapersOnLine, vol. 49, no. 18, pp. 710–715, 2016.
  22. N. M. Mangan, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Inferring biological networks by sparse identification of nonlinear dynamics,” IEEE Transactions on Molecular, Biological and Multi-Scale Communications, vol. 2, no. 1, pp. 52–63, 2016.
  23. M. Quade, M. Abel, J. Nathan Kutz, and S. L. Brunton, “Sparse identification of nonlinear dynamics for rapid model recovery,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 28, no. 6, 2018.
  24. H. K. Chu and M. Hayashibe, “Discovering interpretable dynamics by sparsity promotion on energy and the lagrangian,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 2154–2160, 2020.
  25. J.-C. Loiseau and S. L. Brunton, “Constrained sparse galerkin regression,” Journal of Fluid Mechanics, vol. 838, p. 42–67, 2018.
  26. K. Champion, P. Zheng, A. Y. Aravkin, S. L. Brunton, and J. N. Kutz, “A unified sparse optimization framework to learn parsimonious physics-informed models from data,” IEEE Access, vol. 8, pp. 169259–169271, 2020.
  27. A. A. Kaptanoglu, K. D. Morgan, C. J. Hansen, and S. L. Brunton, “Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches,” Phys. Rev. E, vol. 104, p. 015206, Jul 2021.
  28. Y. Guan, S. L. Brunton, and I. Novosselov, “Sparse nonlinear models of chaotic electroconvection,” Royal Society Open Science, vol. 8, no. 8, p. 202367, 2021.
  29. A. A. Ahmadi and B. El Khadir, “Learning dynamical systems with side information,” in Learning for Dynamics and Control, pp. 718–727, PMLR, 2020.
  30. F. Ghayem, M. Sadeghi, M. Babaie-Zadeh, S. Chatterjee, M. Skoglund, and C. Jutten, “Sparse signal recovery using iterative proximal projection,” IEEE Transactions on Signal Processing, vol. 66, no. 4, pp. 879–894, 2018.
  31. L. Zhang and H. Schaeffer, “On the convergence of the SINDy algorithm,” Multiscale Modeling & Simulation, vol. 17, no. 3, pp. 948–972, 2019.
  32. M. Putinar, “Positive polynomials on compact semi-algebraic sets,” Indiana University Mathematics Journal, vol. 42, no. 3, pp. 969–984, 1993.
  33. http://arxiv.org/abs/1310.4716, 2021. Available from https://github.com/oxfordcontrol/SOSTOOLS.
  34. E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of Atmospheric Sciences, vol. 20, no. 2, pp. 130 – 141, 1963.
  35. E. N. Lorenz, “Computational chaos - a prelude to computational instability,” Physica D: Nonlinear Phenomena, vol. 35, no. 3, pp. 299–317, 1989.
  36. John Wiley & Sons, Ltd, 2019.
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