Bayesian Filtering Learns Lagrangian Dynamics from Noisy Data

Researchers have developed a new approach for understanding the underlying physics of systems, even when the available data is incomplete and contains errors. Their method leverages Bayesian filtering, a technique for estimating unknown variables, to infer the Lagrangian dynamics of a physical system. This involves representing the system's kinetic and potential energies using neural networks, similar to Lagrangian neural networks, but crucially, it treats unmodeled external forces as random noise. This framework transforms the problem into a continuous-time stochastic state-space model. The neural network parameters and the system's actual states are then learned simultaneously using a maximum-likelihood estimation process, enhanced by Gaussian-approximation-based Bayesian filters. The effectiveness of this novel technique has been demonstrated through simulations involving classic physics problems like pendulums and Duffing oscillators, showing improved performance compared to traditional Lagrangian neural networks and other approximate Bayesian filters.