Abstract

Spatio-temporal process models are often used for modelling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to capture using traditional statistical process models such as Gaussian processes. This work proposes the use of Fourier neural operators (FNOs) for constructing statistical dynamical spatio-temporal models for forecasting. An FNO is a flexible mapping of functions that approximates the solution operator of possibly unknown linear or non-linear partial differential equations (PDEs) in a computationally efficient manner. It does so by training on samples of inputs and their respective outputs, and hence explicit knowledge of the underlying PDE is not required. Through simulations from a nonlinear PDE with a known solution, we compare FNO forecasts to those from state-of-the-art statistical spatio-temporal-forecasting methods. Further, using precipitation data in central Europe, we demonstrate the ability of FNO-based dynamic spatio-temporal (DST) statistical modelling to capture complex real-world spatio-temporal dependencies. The research presented in this talk is joint with Dr Pratik Nag (University of Wollongong, Australia), Associate Professor Andrew Zammit Mangion (University of New South Wales, Australia), and Professor Sumeetpal Singh (University of Wollongong, Australia)