Sparse Identification of Nonlinear Dynamical Systems via Reweighted
$\ell_1$-regularized Least Squares
- URL: http://arxiv.org/abs/2005.13232v1
- Date: Wed, 27 May 2020 08:30:15 GMT
- Title: Sparse Identification of Nonlinear Dynamical Systems via Reweighted
$\ell_1$-regularized Least Squares
- Authors: Alexandre Cortiella, Kwang-Chun Park, and Alireza Doostan
- Abstract summary: This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear systems from noisy state measurements.
The aim of this work is to improve the accuracy and robustness of the method in the presence of state measurement noise.
- Score: 62.997667081978825
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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. The idea behind using weighted
$\ell_1$-norm for regularization -- instead of the standard $\ell_1$-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 $\ell_1$-regularized
least squares strategy with respect to state measurement noise, thus
illustrating its viability for a wide range of potential applications.
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