Sparse Identification of Lagrangian for Nonlinear Dynamical Systems via Combinatorial Operation Network (CombOpNet)

Author(s) Information

Allan Pham, California Polytechnic State University, San Luis ObispoFollow

College - Author 1

College of Engineering

Department - Author 1

Mechanical Engineering Department

Advisor

Siyuan “Simon” Xing, College of Engineering, Mechanical Engineering Department

Funding Source

Cal Poly's College of Engineering Dean's Innovation Fund, Paul & Sandi Bonderson, Kim Vorrath, and The Sprague Foundation

Date

10-2025

Abstract/Summary

This research project aims to extend the Combinatorial Operation Neural Network (CombOpNet) framework to discover Lagrangian of high-dimensional nonlinear dynamical systems from data. While recent advances in data-driven methods have shown promising results in recovering governing differential equations, most approaches focus on identifying the vectorized state-space representation rather than the underlying Lagrangian structure. The Lagrangian formulation provides deeper physical insights, such as conservation laws and symmetries, which are crucial for understanding complex phenomena in physics and engineering. By leveraging our recently developed CombOpNet architecture and modifying it to identify variational principles, this project will develop a novel data-driven framework capable of extracting interpretable Lagrangian formulations. This approach will be validated on several benchmark systems and then applied to more complex nonlinear lattice models that are prevalent in condensed matter physics and nonlinear optics.

October 1, 2025.