Implement Spherical Fourier Neural Operator (SFNO)

Summary

Implement SFNO, which uses spherical harmonic transforms instead of FFT for learning operators on spherical domains.

Reference

• Bonev et al., "Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere," ICML 2023. arXiv:2306.03838

Description

SFNO replaces FFT with differentiable Spherical Harmonic Transforms (SHT) to properly handle data on spherical geometry without artifacts from equirectangular projection. It is the backbone of NVIDIA's FourCastNet weather forecasting model and is stable for year-long autoregressive rollouts.

This would require:

• A new SphericalHarmonicTransform implementing the AbstractTransform interface in src/transform.jl
• Integration with existing OperatorConv / OperatorKernel layers
• A Julia SHT implementation or bindings (e.g., via FastTransforms.jl or similar)

Start in src/transform.jl by reading the AbstractTransform interface, then inspect the existing OperatorConv and OperatorKernel layers to understand their integration points. Evaluate a Julia Spherical Harmonic Transform implementation or bindings such as FastTransforms.jl. Done means adding SphericalHarmonicTransform support for spherical domains and integrating it with those layers.