# SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study

arXiv: https://arxiv.org/abs/2403.00578 · HTML: https://mlsanity.com/paper/2403.00578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 1 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [Koopman-based lifting techniques for nonlinear systems identification](https://mlsanity.com/paper/1709.02003/) (2017)
- [SINDy with Control: A Tutorial](https://mlsanity.com/paper/2108.13404/) (2021)
- [Neural Ordinary Differential Equations for Nonlinear System Identification](https://mlsanity.com/paper/2203.00120/) (2022)
- [Convergence of weak-SINDy Surrogate Models](https://mlsanity.com/paper/2209.15573/) (2022)
- [Fitting Jump Models](https://mlsanity.com/paper/1711.09220/) (2017)

## 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.