Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with
  Physics Prior
Thomas Beckers Jacob Seidman Paris Perdikaris George J. Pappas
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.