Integrating Partial Physics Knowledge into Compositional Gaussian Processes

The fusion of physical knowledge with data-driven learning has allowed modelling practitioners to combine fundamental governing laws with the expressivity of machine learning, giving rise to “hybrid” models that have explanatory power where data is missing, whilst retaining the broad learning ability of machine learning technologies. There is thus great value in methods of this nature when attempting to model the behaviour of high value aerospace and civil assets, where data are often lacking, but one is still reliant on the flexibility of data-driven modelling. When constructing hybrid models, the form in which the domain insight exists is critical, as it governs the route by which knowledge is embedded into the model architecture. In many scenarios, this knowledge will not represent the entirety of the phenomena of interest, resulting in only a partial understanding of the driving physics. In this work, we consider how partial knowledge may be integrated into compositional, or deep Gaussian process models. In such model structures, individual Gaussian processes are stacked together as individual layers, where the output of one is fed as the input to another. Whilst embedding physical structure inside single layer Gaussian processes is a very active research area, less attention has been directed to integrating prior knowledge inside compositional architectures. Different opportunities for incorporating physics into compositional architectures will be discussed, before considering their application to modelling dynamic engineering systems, paying particular attention to the quantification of uncertainty across layers.