Differentiable Sparse Identification of Lagrangian Dynamics

TL;DR

This paper introduces a differentiable sparse identification framework for Lagrangian dynamics that improves robustness to noise and complex nonlinearities using B-spline approximation and physical constraints.

Contribution

It integrates cubic B-spline approximation into Lagrangian system identification, enhancing accuracy and noise robustness in discovering complex nonlinear dynamics.

Findings

Outperforms baseline methods in noisy data scenarios

Accurately captures complex nonlinearities in mechanical systems

Reduces noise sensitivity through recursive derivative computation

Abstract

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise sensitivity in complex mechanical systems. The Lagrangian formalism offers a promising alternative, as it typically avoids rational expressions and provides a more concise representation of system dynamics. However, existing Lagrangian identification methods are significantly affected by measurement noise and limited data availability. This paper presents a novel differentiable sparse identification framework that addresses these limitations through three key contributions: (1) the first integration of cubic B-Spline approximation into Lagrangian system identification, enabling accurate representation of complex nonlinearities, (2) a robust equation discovery mechanism that effectively utilizes measurements while incorporating known physical constraints, (3) a recursive derivative computation scheme based on B-spline basis functions, effectively constraining higher-order derivatives and reducing noise sensitivity on second-order dynamical systems. The proposed method demonstrates superior performance and enables more accurate and reliable extraction of physical laws from noisy data, particularly in complex mechanical systems compared to baseline methods.