arXiv:2606.00677v1 Announce Type: new 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 $S>s$: 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
This research is emerging as AI models are increasingly deployed in real-world applications requiring reliable performance across varied conditions, pushing the boundaries of current assumptions.
It highlights an overlooked limitation in a prominent AI architecture (FNOs), impacting how such models should be trained and deployed for optimal and reliable performance, especially in scientific and industrial applications.
The understanding that Fourier Neural Operators don't inherently generalize across spatial resolutions, suggesting that direct fine-grid inference might not always be superior to simpler upsampling methods.
- · Researchers focusing on robust generalization in AI
- · Developers of multi-resolution AI deployment strategies
- · Computational fluid dynamics (CFD) and scientific computing fields
- · AI models relying solely on naive fine-grid inference assumptions
- · Applications where FNOs are deployed without resolution-specific testing
Increased focus on testing and validating resolution equivariance in new AI model architectures.
Development of hybrid inference strategies that dynamically choose between direct fine-grid inference and coarse-grid-plus-upsampling based on performance metrics.
Potential for new FNO architectures specifically designed to overcome this resolution equivariance limitation, leading to more robust scientific AI tools.
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Read at arXiv cs.LG