Green-Routed Neural Operators:\\Physics Determines Where the Network Reads

Excerpt

arXiv:2610.05337v1 Announce Type: cross Abstract: We identify a mismatch between the physical role of transport fields in many PDEs and their usual role in neural operators: PDEs use them to select read coordinates, whereas neural operators typically treat them only as input values. We address this mismatch with the Green-Routed Neural Operator (GRNO), which uses the governing equation to determine where latent features are sampled. A parameter-free equation adapter evaluates the diagnostic rela