Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models

TL;DR

This paper introduces a physics-constrained learning approach that combines Gaussian processes with Port-Hamiltonian models to accurately predict the dynamics of flexible objects while quantifying uncertainty.

Contribution

It presents a novel method integrating physical principles into Gaussian process learning for flexible object dynamics, ensuring trustworthiness and uncertainty quantification.

Findings

Successfully models complex soft object dynamics.

Provides reliable uncertainty estimates.

Preserves Port-Hamiltonian system structure.

Abstract

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.