Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance
Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen. However, before any operator is applied, the grid has already determined how modeling capacity is allocated across space, resolution, and spectral bandwidth. We argue that this hidden design choice should itself be learnable, leading to a question different from standard operator learning: can a surrogate learn where resolution should exist before predicting field evolution? We formulate adaptive discretization as a physics-constrained conditional generation problem over valid mesh displacements. The success of diffusion models in PDE field prediction suggests their pot...
| Authors | Zixuan Shen, Bingchuan Wang, Zhi Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 July 2026 |
| Last updated at source | 13 July 2026 |
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