Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)

TL;DR

SINDy-SI is a novel iterative method that combines SOS programming and side information to identify sparse, physically consistent nonlinear dynamical models with strong generalization capabilities.

Contribution

It introduces an iterative approach that enforces physical laws via side information and promotes sparsity, improving model accuracy and generalization over existing methods.

Findings

Models obey physical laws due to side information constraints.

Sparse polynomial models generalize well beyond training data.

SINDy-SI outperforms traditional system identification techniques.

Abstract

Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.