A Bayesian framework for discovering interpretable Lagrangian of
  dynamical systems from data
Tapas Tripura Souvik Chakraborty
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.