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SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study (2403.00578v1)
Published 1 Mar 2024 in eess.SY, cs.LG, and cs.SY
Abstract: 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.
- Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders. Proc. R. Soc. A: Math. Phys. Eng. Sci., 479(2276), 20230422.
- Fitting jump models. Automatica, 96, 11–21.
- Bouc, R. (1967). Forced vibration of mechanical systems with hysteresis.
- Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS, 113(15), 3932–3937.
- Sparse identification of nonlinear dynamics with control (SINDYc). IFAC-PapersOnLine, 49(18), 710–715. 10th IFAC Symposium on Nonlinear Control Systems NOLCOS 2016.
- Data-driven discovery of coordinates and governing equations. Proceedings of the National Academy of Sciences, 116(45), 22445–22451. 10.1073/pnas.1906995116.
- SINDy with control: A tutorial. In 2021 60th IEEE Conf. on Decision and Control (CDC), 16–21.
- Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478(2260), 20210904. 10.1098/rspa.2021.0904.
- A clustering technique for the identification of piecewise affine systems. Automatica, 39(2), 205–217.
- Continuous-time system identification with neural networks: Model structures and fitting criteria. European Journal of Control, 59, 69–81.
- Data-based hybrid modelling of the component placement process in pick-and-place machines. Control Engineering Practice, 12(10), 1241–1252.
- SINDy-PI: A robust algorithm for parallel implicit sparse identification of nonlinear dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2242), 20200279. 10.1098/rspa.2020.0279.
- Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proc. R. Soc. A., 474(2219), 20180335.
- PySINDy: A comprehensive python package for robust sparse system identification. Journal of Open Source Software, 7.
- Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy. Nuclear Fusion, 63(4), 046015.
- Learning nonlinear state–space models using autoencoders. Automatica, 129, 109666.
- Koopman-based lifting techniques for nonlinear systems identification. IEEE Trans. on Automatic Control, 65(6), 2550–2565.
- Weak SINDy: Galerkin-Based Data-Driven Model Selection. Multiscale Modeling & Simulation, 19(3), 1474–1497. 10.1137/20M1343166.
- Hysteretic Benchmark with a Dynamic Nonlinearity. 10.4121/12967592.
- Neural Ordinary Differential Equations for Nonlinear System Identification. In 2022 American Control Conference (ACC), 3979–3984. 10.23919/ACC53348.2022.9867586.
- Using noisy or incomplete data to discover models of spatiotemporal dynamics. Physical Review E, 101(1), 010203.
- Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nat Mach Intell, 1, 206–215.
- Convergence of weak-SINDy surrogate models. doi.org/10.48550/arXiv.2209.15573.
- Comparing system identification techniques for identifying human-like walking controllers. Royal Society Open Science, 8(12), 211031.
- Three benchmarks addressing open challenges in nonlinear system identification. IFAC-PapersOnLine, 50(1), 446–451. 20th IFAC World Congress.
- Cascaded tanks benchmark combining soft and hard nonlinearities. 10.4121/12960104.V1.
- Uncovering differential equations from data with hidden variables. Physical Review E, 105(5), 054209.
- Optimization assisted kalman filter for cancer chemotherapy dosage estimation. Artificial Intelligence in Medicine, 119.
- On evolutionary system identification with applications to nonlinear benchmarks. Mechanical Systems and Signal Processing, 112, 194–232.
- On the convergence of the SINDy algorithm. Multiscale Modeling & Simulation, 17(3), 948–972.