A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data
This work addresses the need for interpretable and uncertainty-aware methods in learning physical laws from data, offering incremental improvements over existing neural network-based approaches.
The authors tackled the problem of learning interpretable Lagrangian descriptions of dynamical systems from limited data by proposing a sparse Bayesian framework, which yields interpretable results, quantifies uncertainty, and automates Hamiltonian distillation, as demonstrated across six examples.
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.