SciML / SciML/NeuralOperators.jl
Implement NORM (Neural Operator on Riemannian Manifolds)
Nobody has claimed this yet.
- Dominant language
- Julia
- Stars
- 41
- Forks
- 15
- Avg merge
- 13h 14m
- Merged PRs (30d)
- 12
Description
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.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reading the linked 2024 NORM paper and comparing its requirements with the existing NeuralOperators.jl structure. The issue names no files, tests, entry points, or acceptance criteria, so identify the appropriate operator extension point and define validation for Laplace-Beltrami eigenfunction mappings before implementation.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- machine-learning
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100