Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior
This work addresses the need for more data-efficient and physically correct models in dynamics modeling, though it appears incremental as it builds on existing Port-Hamiltonian systems with a Bayesian twist.
The authors tackled the problem of data-driven models neglecting physical principles by proposing Gaussian Process Port-Hamiltonian systems (GP-PHS), a physics-informed Bayesian learning approach that generates passive systems with uncertainty quantification.
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.