Implement Latent Neural Operator

Summary

Implement the Latent Neural Operator, which uses Physics-Cross-Attention (PhCA) to learn operators in a compressed latent space.

Reference

• Wang et al., "Latent Neural Operator for Solving Forward and Inverse PDE Problems," NeurIPS 2024. arXiv:2406.03923

Description

The Latent Neural Operator transforms input function representations from geometric space to a compressed latent space via Physics-Cross-Attention (PhCA), processes them with latent-space operator layers, then maps back. This achieves 50% GPU memory reduction and 1.8x training speedup compared to full-space operators, while achieving highest precision on multiple benchmarks.

Key components:

• Physics-Cross-Attention (PhCA) encoder/decoder between geometric and latent spaces
• Latent-space operator layers (can use FNO or attention)
• Applicable to both forward and inverse problems

Start by reading the referenced NeurIPS 2024 paper and the repository's existing Neural Operator implementations. Define the PhCA encoder and decoder, latent-space operator layers, and support for forward and inverse problems. Done means the Latent Neural Operator is implemented with the described geometric-to-latent-to-geometric flow and its claimed use cases are covered.