Gaussian process kernels for partial physical insight

Fusing known physics into data-driven learners allows modelling practitioners to combine the expressive power of traditional machine learning with known mechanistic laws, where the objective is to enhance predictive performance, interpretability, and model generalisation. A core consideration that must be made when implementing a physics-informed learning architecture is how relevant knowledge will be embedded into the model structure, which, generally, is informed by the type of physics that is available. Frequently this knowledge may not be complete, with only a partial understanding of the governing physics available. In this work, possible paths for deriving Gaussian process kernels that are representative of partial knowledge will be considered. How the type of knowledge that is possessed influences the derivation will be explored, particularly when there is the potential for some aspect of misspecified physics. An example of deriving partially structured kernels will be investigated for modelling the decoupled response of a GARTEUR laboratory aircraft structure, where the derived kernels are used to decompose the dynamics of the aircraft into modal contributions.