Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems

TL;DR

This paper introduces Gaussian process latent force models that combine physical models with non-parametric Gaussian processes to improve learning and stochastic control of systems with unknown inputs, offering new theoretical insights.

Contribution

It presents a hybrid modeling framework integrating physical models and Gaussian processes, along with new theoretical results on observability and controllability.

Findings

Developed a stochastic control methodology for LFMs

Provided new theoretical results on observability and controllability

Reviewed inference and learning methods for LFMs

Abstract

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first-principles physical model part and a non-parametric GP model part. We briefly review the statistical inference and learning methods for this kind of models, introduce stochastic control methodology for the models, and provide new theoretical observability and controllability results for them.