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.

arXiv commentAccepted at the IEEE Conference on Decision and Control 2022

References in corpus (6)

• Hamiltonian Neural Networks
• On Learning Hamiltonian Systems from Data
• Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems
• Symplectic Gaussian Process Regression of Hamiltonian Flow Maps
• Equilibrium Distributions and Stability Analysis of Gaussian Process State Space Models
• Learning ODE Models with Qualitative Structure Using Gaussian Processes

Cited by in corpus (1)

• Combining Federated Learning and Control: A Survey