Discovering interpretable Lagrangian of dynamical systems from data

TL;DR

This paper introduces a novel machine learning framework for discovering interpretable Lagrangians from data, enabling better understanding of physical systems and their conservation laws, with generalization to complex systems.

Contribution

It presents a new data-driven method for learning interpretable Lagrangians that generalize across different system complexities, improving interpretability and reusability.

Findings

Successfully derived Lagrangians for ODE and PDE systems

Automated discovery of conservation laws

Framework generalizes from subsets to infinite-dimensional systems

Abstract

A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing equations of motion. The generalization of equation discovery techniques has huge potential; however, existing Lagrangian discovery frameworks are black-box in nature. This raises a concern about the reusability of the discovered Lagrangian. In this article, we propose a novel data-driven machine-learning algorithm to automate the discovery of interpretable Lagrangian from data. The Lagrangian are derived in interpretable forms, which also allows the automated discovery of conservation laws and governing equations of motion. The architecture of the proposed framework is designed in such a way that it allows learning the Lagrangian from a subset of the underlying domain and then generalizing for an infinite-dimensional system. The fidelity of the proposed framework is exemplified using examples described by systems of ordinary differential equations and partial differential equations where the Lagrangian and conserved quantities are known.