Model Inversion for Spatio-temporal Processes using the Fourier Neural Operator

We explore model inversion using the Fourier Neural Operator (FNO) of Li et al. The approach learns a FNO emulator of the partial differential equation forward operator from simulated realisations and then the latent inputs (physical system parameters) are selected by solving an optimisation to match a set of observations. Our results suggest that this underdetermined inverse problem is substantially harder but by careful regularisation we are able to improve our inference substantially.