Modelling Atmospheric Dynamics with Spherical Fourier Neural Operators

Fourier Neural Operators (FNOs) have established themselves as an efficientmethod for learning resolution-independent operators in a wide range of scientificmachine learning applications. This can be attributed to their ability to effectivelymodel long-range dependencies in spatio-temporal data through computationally ef-ficient global convolutions. However, the use of discrete Fourier transforms (DFTs)in FNOs leads to spurious artifacts and pronounced dissipation when applied tospherical coordinates, due to the incorrect assumption of flat geometry. To ad-dress the issue, we introduce Spherical FNOs (SFNOs), which use the generalizedFourier transform for learning operators on spherical geometries. We demonstratethe effectiveness of the method for forecasting atmospheric dynamics, producingstable auto-regressive results for a simulated time of one year (1,460 steps) whileretaining physically plausible dynamics. This development has significant implica-tions for machine learning-based climate dynamics emulation, which could play acrucial role in accelerating our response to climate change.