mlsanityData to 14 Oct 2026

Euclidean Fourier Neural Operators

arXiv 2608.28425 ↗First posted 28 Aug 2026cs.LG cond-mat.mtrl-sci physics.comp-phcited by 0

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Abstract (arXiv)

Fourier neural operators (FNOs) provide an efficient framework for learning mappings between function spaces as they are, by construction, independent of the grid resolution at which they are trained and evaluated. However, FNOs are not independent of the periodic domain they are applied to: their discrete spectral weights are indexed by integer Fourier mode numbers, which correspond to physical wavevectors. When applied to a different domain, the same trained weights act at different wavevectors, and the FNO silently represents a different operator. This makes FNOs unsuitable for tasks where transfer across domains is crucial. We propose Euclidean Fourier neural operators~(EFNOs) as a domain-independent alternative to FNOs. By parameterizing the spectral kernel as a continuous function of the physical wavevector, the EFNO can learn operators that act consistently across periodic domains of varying shape and size. We evaluate the EFNO on a simple heat equation and on a practically relevant materials science task of learning exchange-correlation potentials across different crystal structures, and demonstrate that the EFNO is able to generalize to unseen grid sizes and domains.

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References · 15

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  4. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  6. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 233
  7. 2021Seismic wave propagation and inversion with Neural Operatorscited by 51
  8. 2023Domain Agnostic Fourier Neural Operatorscited by 38
  9. 2023Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domainscited by 21
  10. 2024Gaussian Plane-Wave Neural Operator for Electron Density Estimationcited by 9
  11. 2022Pseudo-Differential Neural Operator: Generalized Fourier Neural Operator for Learning Solution Operators of Partial Differential Equationscited by 8
  12. 2025KANO: Kolmogorov-Arnold Neural Operatorcited by 7
3 more
  1. 2026Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theorycited by 2
  2. 2026SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operatorscited by 1
  3. 2026Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domainscited by 1

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