mlsanityData to 7 Oct 2026

Non-equispaced Fourier Neural Solvers for PDEs

arXiv 2212.04689 ↗First posted 9 Dec 2022cs.LGcited by 8

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Abstract (arXiv)

Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is sometimes inevitably non-equispaced in real-world systems, limiting their applicability. In this paper, we propose a Non-equispaced Fourier PDE Solver (textscNFS) with adaptive interpolation on resampled equispaced points and a variant of Fourier Neural Operators as its components. Experimental results on complex PDEs demonstrate its advantages in accuracy and efficiency. Compared with the spatially-equispaced benchmark methods, it achieves superior performance with 42.85% improvements on MAE, and is able to handle non-equispaced data with a tiny loss of accuracy. Besides, to our best knowledge, textscNFS is the first ML-based method with mesh invariant inference ability to successfully model turbulent flows in non-equispaced scenarios, with a minor deviation of the error on unseen spatial points.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 38 of its 52 references that are in the map. First posted on arXiv 9 Dec 2022.

Builds on

38 of 52 references.

References · 38

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8 papers.

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