New kernels improve modeling of spatially varying physical systems
Structure-Aware Spatial Kernels for Gaussian Process Distributed Port-Hamiltonian Systems
Machine Learning
Summary
Modeling physical systems that change over space is often tough because existing methods assume things are the same everywhere. The authors created new mathematical tools, called structure-aware kernels, that better capture how things vary in space without needing exact formulas. They tested their approach on models of a vibrating string with changing stiffness and found it made predictions more accurate. This helps machine learning better understand systems that have complex spatial behavior.
What this means in practice
- •For control system engineers: Improve data-driven models for mechanical systems with spatially varying properties to better predict and control their behavior.
- •For robotic system developers: Enhance simulation and control accuracy for robots interacting with environments that have spatially changing stiffness or compliance.
Authors
Tianyi Yang, Thomas Beckers
Abstract
Gaussian process distributed port-Hamiltonian systems (GP-dPHS) enable data-driven modeling of distributed dynamical systems while preserving their physical structure. However, standard stationary kernels can be inefficient for spatially heterogeneous systems because they neither exploit known input invariances nor reflect structured spatial dependencies. We address this limitation with a structure-aware kernel design that removes irrelevant state coordinates and decouples state and spatial dependencies through a tensor-product covariance. This modular construction allows qualitative knowledge of spatial heterogeneity to be incorporated by selecting an appropriate spatial kernel without requiring an analytical description of the underlying profile. Numerical experiments on a nonlinear string with periodic, smoothly varying, and semi-piecewise stiffness profiles demonstrate that structural decoupling consistently improves reconstruction accuracy, while profile-matched spatial kernels yield substantially larger gains in force-field and trajectory reconstruction.