Spherical Fourier Neural Operators: Learning Stable Dynamics on the
  Sphere
Boris Bonev Thorsten Kurth Christian Hundt Jaideep Pathak Maximilian Baust Karthik Kashinath Anima Anandkumar
Fourier Neural Operators (FNOs) have proven to be an efficient and effective
method for resolution-independent operator learning in a broad variety of
application areas across scientific machine learning. A key reason for their
success is their ability to accurately model long-range dependencies in
spatio-temporal data by learning global convolutions in a computationally
efficient manner. To this end, FNOs rely on the discrete Fourier transform
(DFT), however, DFTs cause visual and spectral artifacts as well as pronounced
dissipation when learning operators in spherical coordinates since they
incorrectly assume a flat geometry. To overcome this limitation, we generalize
FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators
on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics,
and demonstrate stable auto\-regressive rollouts for a year of simulated time
(1,460 steps), while retaining physically plausible dynamics. The SFNO has
important implications for machine learning-based simulation of climate
dynamics that could eventually help accelerate our response to climate change.