Weak-form modified sparse identification of nonlinear dynamics

TL;DR

This paper introduces WmSINDy, a novel method combining weak SINDy and mSINDy to enhance nonlinear system identification and noise modeling, especially under strong noise conditions.

Contribution

The paper proposes WmSINDy, integrating weak SINDy with mSINDy, to improve robustness and accuracy in identifying nonlinear dynamics and noise distributions.

Findings

WmSINDy outperforms baseline methods in accuracy.

It effectively characterizes noise in nonlinear systems.

Demonstrates robustness in high-noise environments.

Abstract

Identifying nonlinear dynamics and characterizing noise from data is critical across science and engineering for understanding and modeling the behavior of the systems accurately. The modified sparse identification of nonlinear dynamics (mSINDy) has emerged as an effective framework for identifying systems embedded in heavy noise; however, further improvements can expand its capabilities and robustness. By integrating the weak SINDy (WSINDy) into mSINDy, we introduce the weak mSINDy (WmSINDy) to improve the system identification and noise modeling by harnessing the strengths of both approaches. The proposed algorithm simultaneously identifies parsimonious nonlinear dynamics and extracts noise probability distributions using automatic differentiation. We evaluate WmSINDy using several nonlinear systems and it demonstrates improved accuracy and noise characterization over baselines for systems embedded in relatively strong noise.