From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning
Neural operators have become a central tool for solving partial differential equations (PDEs), with spectral operators offering efficient global mixing across spatial locations. However, many PDEs contain physics-sensitive local structures that are critical to the underlying physical behavior. For example, in Darcy flow, local material interfaces are often reflected by sharp changes in the permeability field and can strongly influence the solution. Existing spectral operators primarily adapt modal mixing based on center-point representations, making them insufficiently responsive to such localized structural variations. We propose the Edge-Conditioned Spectral Operator (ESO), a novel spec...
| Authors | Zhentao Tan, Ruijie Quan, Yi Yang |
|---|---|
| Primary category | cs.AI |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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