HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
Principled approaches for extending neural architectures to function spaces for operator learning
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Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
Fourier Neural Operators lack reliable zero-shot resolution equivariance on Darcy flow; direct inference at higher resolution can underperform low-resolution inference plus upsampling.
citing papers explorer
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Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
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Learning Neural Operator Surrogates for the Black Hole Accretion Code
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
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Limits of Resolution Equivariance in Fourier Neural Operators
Fourier Neural Operators lack reliable zero-shot resolution equivariance on Darcy flow; direct inference at higher resolution can underperform low-resolution inference plus upsampling.