A spectrum of physics-informed Gaussian processes for regression in
  engineering
Elizabeth J Cross Timothy J Rogers Daniel J Pitchforth Samuel J Gibson Matthew R Jones
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.