Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models
This addresses the challenge of trustworthy and generalizable modeling for flexible objects in applications such as soft robotics, representing an incremental improvement by integrating existing methods.
The paper tackles the problem of modeling the complex, nonlinear dynamics of flexible objects like those in soft robotics by proposing a physics-constrained learning method that combines Gaussian processes with Port-Hamiltonian models, enabling uncertainty quantification and preserving system compositionality.
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.