Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere

TL;DR

This paper introduces Spherical Fourier Neural Operators (SFNOs), an extension of FNOs designed for spherical geometries, enabling stable and physically plausible long-term forecasting of atmospheric dynamics, with potential applications in climate modeling.

Contribution

The paper develops SFNOs to address limitations of FNOs on spherical domains, improving stability and accuracy in modeling spherical data such as climate dynamics.

Findings

SFNOs enable stable year-long atmospheric forecasts.

SFNOs produce physically plausible climate simulations.

The method improves long-range dependency modeling on spheres.

Abstract

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.