Sparse identification of Lagrangian for nonlinear dynamical systems via proximal gradient method.

Area of Science:

• * Physics
• * Computational Science
• * Mechanical Engineering

Background:

• * Data-driven modeling aims to autonomously discover physical laws from experimental data.
• * Sparse regression techniques like sparse identification of nonlinear dynamics (SINDy) are effective but struggle with rational functions and noise.
• * Extracting Lagrangians offers a more concise representation of system dynamics, particularly for mechanical systems.

Purpose of the Study:

• * To develop a robust method for extracting the Lagrangian of dynamical systems from noisy measurement data.
• * To enhance the capabilities of existing Lagrangian-SINDy methods to handle noise effectively.
• * To provide a noise-tolerant computational tool for discovering explicit dynamics laws.

Main Methods:

• * Developed an extended Lagrangian-SINDy (xL-SINDy) method incorporating SINDy principles.
• * Utilized the proximal gradient method for sparse Lagrangian expression identification.
• * Validated the method's performance against varying noise levels in four distinct mechanical systems.

Main Results:

• * xL-SINDy demonstrated superior robustness in extracting governing equations from noisy data compared to existing methods.
• * The method effectively identified dynamical system Lagrangians even under significant noise.
• * Performance was benchmarked against SINDy-PI, a robust SINDy variant for implicit dynamics.

Conclusions:

• * xL-SINDy offers a significant advancement in noise-tolerant computational methods for physics discovery.
• * The approach is highly effective for extracting nonlinear mechanical system dynamics from experimental data.
• * This work paves the way for more reliable data-driven discovery of physical laws in the presence of noise.