Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior
Abstract
Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.
Keywords
Cite
@article{arxiv.2305.09017,
title = {Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior},
author = {Thomas Beckers and Jacob Seidman and Paris Perdikaris and George J. Pappas},
journal= {arXiv preprint arXiv:2305.09017},
year = {2023}
}
Comments
Accepted at the IEEE Conference on Decision and Control 2022