Physically-informed change-point kernels for structural dynamics

Abstract: The relative balance between physics and data within any physics-informed machine learner is an important modelling consideration to ensure that the benefits of both physics and data-based approaches are maximised. An over reliance on physical knowledge can be detrimental, particularly when the physics-based component of a model may not accurately represent the true underlying system. An underutilisation of physical knowledge potentially wastes a valuable resource, along with benefits in model interpretability and reduced demand for expensive data collection. Achieving an optimal physics-data balance is a challenging aspect of model design, particularly if the level varies through time; for example, one might have a physical approximation, only valid within particular regimes, or a physical phenomenon may be known to only occur when given conditions are met (e.g. at high temperatures). This paper develops novel, physically-informed, change-point kernels for Gaussian processes, capable of dynamically varying the reliance upon available physical knowledge. A high level of control is granted to a user, allowing for the definition of conditions in which they believe a phenomena should occur and the rate at which the knowledge should be phased in and out of a model. In circumstances where users may be less certain, the switching reliance upon physical knowledge may be automatically learned and recovered from the model in an interpretable and intuitive manner. Variation of the modelled noise based on the physical phenomena occurring is also implemented to provide a more representative capture of uncertainty alongside predictions. The capabilities of the new kernel structures are explored through the use of two engineering case studies: the directional wind loading of a cable-stayed bridge and the prediction of aircraft wing strain during in-flight manoeuvring.