Iterative Sparse Identification of Nonlinear Dynamics

TL;DR

This paper introduces iterative SINDy, an enhanced method for identifying nonlinear dynamical systems that reduces computational costs and handles high-dimensional data effectively, while maintaining accuracy.

Contribution

The paper proposes an iterative expansion and compression approach for the SINDy dictionary, improving scalability and efficiency for high-dimensional datasets.

Findings

Iterative SINDy achieves similar accuracy to traditional SINDy.

It significantly reduces computational complexity.

Effective for high-dimensional time-series data.

Abstract

In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with a minimal number of terms, utilizing the principles of compressive sensing. This feature, which relies on a small number of terms, is crucial for interpretability. The effectiveness of SINDy hinges on the choice of candidate functions within its dictionary to extract governing equations of dynamical systems. A larger dictionary allows for more terms, enhancing the quality of approximations. However, the computational complexity scales with dictionary size, rendering SINDy less suitable for high-dimensional datasets, even though it has been successfully applied to low-dimensional datasets. To address this challenge, we introduce iterative SINDy in this paper, where the dictionary undergoes expansion and compression through iterations. We also conduct an analysis of the convergence properties of iterative SINDy. Simulation results validate that iterative SINDy can achieve nearly identical performance to SINDy, while significantly reducing computational complexity. Notably, iterative SINDy demonstrates effectiveness with high-dimensional time-series data without incurring the prohibitively high computational cost associated with SINDy.