Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

• URL: http://arxiv.org/abs/2305.09017v1
• Date: Mon, 15 May 2023 20:59:41 GMT
• Title: Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior
• Authors: Thomas Beckers, Jacob Seidman, Paris Perdikaris, George J. Pappas
• Abstract summary: Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. These models often neglect basic physical principles which determine the behavior of any real-world system. We propose a physics-informed Bayesian learning approach with uncertainty quantification.
• Score: 17.812064311297117
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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