# Sparse Identification of Nonlinear Dynamical Systems via Reweighted ℓ1-regularized Least Squares

arXiv: https://arxiv.org/abs/2005.13232 · HTML: https://mlsanity.com/paper/2005.13232/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2020.

## Built on by (most cited first, 21 of 21)

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- [Automating the Discovery of Partial Differential Equations in Dynamical Systems](https://mlsanity.com/paper/2404.16444/) (2024)
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- [Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction](https://mlsanity.com/paper/2605.12683/) (2026)
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## Abstract (arXiv)

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics (SINDy) approach of it [Brunton et al., PNAS, 113 (15) (2016) 3932-3937], which relies on two main assumptions: the state variables are known it a priori and the governing equations lend themselves to sparse, linear expansions in a (nonlinear) basis of the state variables. The aim of this work is to improve the accuracy and robustness of SINDy in the presence of state measurement noise. To this end, a reweighted ℓ1-regularized least squares solver is developed, wherein the regularization parameter is selected from the corner point of a Pareto curve. The idea behind using weighted ℓ1-norm for regularization -- instead of the standard ℓ1-norm -- is to better promote sparsity in the recovery of the governing equations and, in turn, mitigate the effect of noise in the state variables. We also present a method to recover single physical constraints from state measurements. Through several examples of well-known nonlinear dynamical systems, we demonstrate empirically the accuracy and robustness of the reweighted ℓ1-regularized least squares strategy with respect to state measurement noise, thus illustrating its viability for a wide range of potential applications.