A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data

TL;DR

This paper introduces a Bayesian method for learning interpretable Lagrangian descriptions of physical systems from limited data, enabling uncertainty quantification and derivation of Hamiltonian and PDE models.

Contribution

It presents a sparse Bayesian framework that yields interpretable Lagrangians, quantifies uncertainty, and automates Hamiltonian extraction, advancing beyond neural network-based approaches.

Findings

Effective in six different physical system examples

Provides interpretable and uncertainty-aware models

Automates Hamiltonian and PDE derivations

Abstract

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of Hamiltonian and Lagrangian of physical systems. While the existing methods parameterize the Lagrangian using neural networks, we propose an alternate framework for learning interpretable Lagrangian descriptions of physical systems from limited data using the sparse Bayesian approach. Unlike existing neural network-based approaches, the proposed approach (a) yields an interpretable description of Lagrangian, (b) exploits Bayesian learning to quantify the epistemic uncertainty due to limited data, (c) automates the distillation of Hamiltonian from the learned Lagrangian using Legendre transformation, and (d) provides ordinary (ODE) and partial differential equation (PDE) based descriptions of the observed systems. Six different examples involving both discrete and continuous system illustrates the efficacy of the proposed approach.