A spectrum of physics-informed Gaussian processes for regression in engineering

TL;DR

This paper introduces a spectrum of physics-informed Gaussian process models that integrate expert knowledge with data-driven regression to improve predictions in engineering systems with limited data, enhancing interpretability and reducing data dependency.

Contribution

It presents a novel spectrum of Gaussian process models that explicitly incorporate physics-based knowledge, advancing the integration of machine learning and physics in engineering regression tasks.

Findings

Reduced data requirements for accurate modeling

Enhanced interpretability of Gaussian process models

Demonstrated effectiveness through engineering examples

Abstract

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as ``big,'' they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a spectrum of possible Gaussian process models are introduced that enable the incorporation of different levels of expert knowledge of a system. Examples illustrate how these approaches can significantly reduce reliance on data collection whilst also increasing the interpretability of the model, another important consideration in this context.