A spectrum of physics-informed Gaussian processes for regression in engineering
This work addresses the problem of data scarcity in engineering modeling, offering incremental improvements by integrating physics into Gaussian processes for enhanced predictions.
The paper tackles the challenge of making predictive models for engineering systems with limited data by combining machine learning with physics-based reasoning, introducing a spectrum of Gaussian process models that incorporate expert knowledge to reduce data reliance and increase interpretability.
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.