FourCastNet: a weather forcasting model using Neural Operators

FourCastNet 1 casts global weather forecasting as a learned, resolution-invariant neural operator: an Adaptive Fourier Neural Operator (AFNO) with a ViT backbone, trained on ERA5 at $0.25^\circ$ and rolled out autoregressively. It replaces the costly $O(N^2)$ self-attention with an $O(N\log N)$ Fourier mixer, but its FFT implicitly assumes a flat domain and distorts at the poles, limiting stable rollouts to $\sim$25 days.

FourCastNet 2 fixes the geometry by replacing the FFT with the Spherical Harmonic Transform (SHT), giving an $SO(3)$-equivariant Spherical Fourier Neural Operator (SFNO). Respecting the sphere’s symmetry yields stable autoregressive rollouts for a full year. It remains deterministic, however, so its forecasts blur toward the ensemble mean and lose fine scales.

FourCastNet 3 makes the model probabilistic and purely convolutional: it augments the SFNO with local DISCO convolutions (anisotropic filters the spectral route cannot represent), and a hidden Markov formulation conditioned on a spherical-diffusion latent generates ensembles in a single forward pass. Trained end-to-end with a combined spatial + spectral CRPS objective on 1024+ GPUs, it matches GenCast and beats IFS-ENS at 8—60$\times$ lower cost, staying sharp and spectrally faithful out to 60 days.

See FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale for details.