Green-Routed Neural Operators: Physics Determines Where the Network Reads
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 relation and constructs a departure map whose values are the read coordinates. A multiscale encoder-decoder combines centered and routed reads of latent features to learn the complete finite-time update. Across five two- and three-dimensional PDE syst...
| Authors | Chenhao Si, Ming Yan |
|---|---|
| Primary category | cs.LG |
| Published | 4 October 2026 |
| Last updated at source | 9 October 2026 |
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