Sparse Identification of Nonlinear Dynamical Systems via Reweighted $\ell_1$-regularized Least Squares

Understand

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 $\ell_1$-regularized least squares solver is developed, wherein the regularization parameter is selected from the corner point of a Pareto curve.