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SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study

arXiv 2403.00578 ↗First posted 1 Mar 2024eess.SY cs.LG cs.SYcited by 0

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Abstract (arXiv)

In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.

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References · 12

  1. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 140
  2. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  3. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  4. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 89
  5. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  6. 2018On the Convergence of the SINDy Algorithmcited by 49
  7. 2020Continuous-time system identification with neural networks: Model structures and fitting criteriacited by 30
  8. 2017Koopman-based lifting techniques for nonlinear systems identificationcited by 18
  9. 2021SINDy with Control: A Tutorialcited by 15
  10. 2022Neural Ordinary Differential Equations for Nonlinear System Identificationcited by 15
  11. 2022Convergence of weak-SINDy Surrogate Modelscited by 11
  12. 2017Fitting Jump Modelscited by 9

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