Implement NORM (Neural Operator on Riemannian Manifolds)

[ChrisRackauckas-Claude]

Summary

Implement NORM, which generalizes neural operators from Euclidean spaces to Riemannian manifolds using Laplacian eigenfunctions.

Reference

• "Learning neural operators on Riemannian manifolds," National Science Open, 2024. DOI: 10.1360/nso/20240001

Description

NORM shifts function-to-function mappings into the subspace of Laplace-Beltrami eigenfunctions on the manifold, then learns finite-dimensional mappings there. This preserves discretization-independence on complex geometries (spheres, surfaces, general manifolds) and naturally extends spectral neural operator methods beyond Euclidean domains.

Related to SFNO (spherical case) but more general. See also GLNO (arXiv:2512.16409) for a Laplace-specific variant on manifolds.