Composable Physics-Informed Learning with Uncertainty Quantification based on Port-Hamiltonian systems

Abstract: Data-driven approaches achieve remarkable results for modeling nonlinear systems 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 consistent. In this talk, I will present our results on physics-constrained Gaussian processes for learning of dynamical system with a focus on the class of electromechanical systems. I will propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-constrained, nonparametric Bayesian learning approach with uncertainty quantification for ODE and PDE systems with unknown dynamics. In contrast to many physics-informed techniques that impose physics by penalty, the proposed data-driven model is physically correct by design. The framework is in particular suitable for composable learning as its structure can be preserved under interconnection. Finally, I demonstrate the application of the model within a robust control framework to enable safe learning-based control.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

( slides | video )

Port-Hamiltonian Seminar

Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY