Physics-derived covariance functions for machine learning in structural dynamics

Abstract This paper attempts to bridge the gap between standard engineering practice and machine learning when modelling stochastic processes. For a number of physical processes of interest, derivation of the (auto)covariance is achievable. This paper suggests their use as priors in a standard Gaussian process regression as a means of enhancing predictive capability in situations where they are reflective of the process of interest. A covariance function of a linear oscillator under random load is derived and used in a regression context to predict the displacements of a vibratory system. A simulation case study is used to demonstrate the enhancement over a standard Gaussian process regression model.