Physically-informed change-point kernels for variable levels of physical knowledge inclusion in Gaussian processes

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 modelled system. An under utilisation of physical knowledge potentially wastes a valuable resource, along with benefits in model interpretability and reduced demand for expensive data collection. Although adjusting the relative levels of physics and data reliance within a model is possible through the adaptation of the model structure, in practice, this can be challenging, with the relative balance produced by new model structures not always clear before they are implemented. This paper presents a means of being able to tune the balance of physics and data reliance within a model through the development of physically-informed change-point kernels for Gaussian processes. These combine more structured physical kernels, capable of enforcing physically derived behaviours, with flexible, general purpose kernels, and provide means to dynamically change the relative levels of reliance on physics and data within a model.