cs.LG · 2607.02088 Copy arXiv ID · Jul 2, 2026 Save Fourier Neural Operators for Rayleigh-Bénard Convection Authors: Chelsea Maria John , Thibaut Lunet , Sebastian Götschel , Andreas Herten , Stefan Kesselheim , Daniel Ruprecht
Organizations: Jülich Supercomputing Centre, Jülich, Germany · Hamburg University of Technology, Hamburg, Germany
Abstract We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-Bénard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline. The resulting model is compact (314k parameters, 1.26 MB) and fast (7 ms inference), while maintaining similar accuracy as demonstrated in previous benchmarks. We show that although FNOs generalize to finer meshes, accuracy remains limited by the resolution of the training data.
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Jun 7, 2026 · math.NA J/K move · Enter open · S save
Jakob Dilen, Alexander Keller, Frances Y. Kuo, Dirk Nuyens
The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces. Its efficient implementation is based on the multi-dimensional Fourier transform. By deriving general regularity bounds for the FNO with respect to both the spatial and parametric variables, we prove that the generalization error of the FNO can be improved by replacing spatial tensor product grids with purpose-built rank-1 lattice points, and by using a second lattice carefully constructed as training points in the parametric space. We achieve more accurate and efficient approximations from fewer network parameters, fewer spatial points, and fewer training samples. In addition, the architecture is simplified, because the high-dimensional Fourier transform on rank-1 lattices requires only a \emph{one-dimensional fast Fourier transform}, and we can use a \emph{hyperbolic cross} frequency index set with lattice points. We demonstrate the benefits of our \emph{lattice-based hyperbolic-cross FNOs} for an elliptic PDE on the torus.