{"ID":2922064,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-02T11:10:10.536057254Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.00677","arxiv_id":"2606.00677","title":"Limits of Resolution Equivariance in Fourier Neural Operators","abstract":"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 $S\u003es$: 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 frequencies, with high-frequency output produced mainly by late nonlinear/decoder stages. This offers a mechanistic explanation for why FNO can perform well while retaining few modes, yet remain sensitive under resolution shifts. Our findings highlight a simple but strong baseline for cross-resolution evaluation and point to nonlinear aliasing as a key obstacle to zero-shot resolution equivariance.","short_abstract":"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 $S\u003es$: running FNO directly at $S$, or run...","url_abs":"https://arxiv.org/abs/2606.00677","url_pdf":"https://arxiv.org/pdf/2606.00677v1","authors":"[\"Alex Colagrande\",\"Paul Caillon\",\"Eva Feillet\",\"Alexandre Allauzen\"]","published":"2026-05-30T11:28:17Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}