Limits of Resolution Equivariance in Fourier Neural Operators
Fourier Neural Operators are often assumed to generalize across spatial resolutions, enabling training on a coarse grid and deployment on a finer grid. We test this assumption by contrasting two inference-time choices when moving from training resolution $s$ to test resolution $S>s$: running FNO directly at $S$, or running at $s$ and upsampling the prediction to $S$ via Fourier zero-padding. On Darcy flow, we observe that direct fine-grid inference is not reliably beneficial and can be worse than the low-grid-plus-upsampling baseline. We further analyze layerwise spectra and find that, under Fourier truncation, intermediate representations increasingly concentrate energy in low frequencie...
| Authors | Alex Colagrande, Paul Caillon, Eva Feillet et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 May 2026 |
| Last updated at source | 30 May 2026 |
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