Physics Enhanced Data-Driven Models With Variational Gaussian Processes

Abstract

Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain knowledge and data provide necessary information about the system. In this paper, we present a data-driven model that takes advantage of partial domain knowledge in order to improve generalization and interpretability. The presented approach, which we call EVGP (Explicit Variational Gaussian Process), has the following advantages: 1) using available domain knowledge to improve the assumptions (inductive bias) of the model, 2) scalability to large datasets, 3) improved interpretability. We show how the EVGP model can be used to learn system dynamics using basic Newtonian mechanics as prior knowledge. We demonstrate how the addition of prior domain-knowledge to data-driven models outperforms purely data-driven models.

Keywords

• Bayesian neural networks
• domain knowledge
• Gaussian process
• uncertainty
• variational inference