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Spherical Fourier neural operators

Contribution grade

Scientific machine learning · Human-designed research method or resource

Reference score145,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Uses spherical-harmonic convolutions rather than planar FFTs for operator learning on spherical geometry, with a differentiable spherical-harmonic implementation and reported stable atmospheric rollouts.

Scientific scope

Uses spherical-harmonic convolutions rather than planar FFTs for operator learning on spherical geometry, with a differentiable spherical-harmonic implementation and reported stable atmospheric rollouts. Seven original authors. SO(3) equivariance pertains to the specified linear spherical layer/continuous construction; discrete nonlinearities are only approximate and the proposed nonlinear frequency variant is not equivariant. Position embeddings and valid transforms constrain grid transfer. Year-long plausible rollouts do not establish climate fidelity or long-horizon trajectory accuracy.

Evidence

The linked original sources describe the stated contribution and its evidence limits. WRS has not independently rerun the experiments or certified a proof. Seven original authors. SO(3) equivariance pertains to the specified linear spherical layer/continuous construction; discrete nonlinearities are only approximate and the proposed nonlinear frequency variant is not equivariant. Position embeddings and valid transforms constrain grid transfer. Year-long plausible rollouts do not establish climate fidelity or long-horizon trajectory accuracy.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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