Implement Geometry-Informed Neural Operator (GINO)

[ChrisRackauckas-Claude]

Summary

Implement GINO, a hybrid GNO + FNO architecture that uses signed distance function (SDF) geometry encoding for large-scale 3D PDEs.

Reference

• Li et al., "Geometry-Informed Neural Operator for Large-Scale 3D PDEs," NeurIPS 2023. arXiv:2309.00583

Description

GINO combines GNO (for irregular input/output grids) with FNO (for efficient spectral processing on regular latent grids). Input geometry is encoded via signed distance functions (SDFs). The architecture maps from irregular mesh → regular latent grid via GNO, processes with FNO layers, then maps back via GNO. Reports 26,000x speedup over GPU-based CFD solvers for automotive aerodynamics.

Depends on graph neural network support (GNNLux) and the existing FNO implementation.