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.
The paper evaluates twelve correction architectures from linear regression to Fourier Neural Operators for 2D anisotropic acoustic wave simulations using a unified 10-fold cross-validation on 27,000 heterogeneous velocity fields.
Fourier Neural Operators lack reliable zero-shot resolution equivariance on Darcy flow; direct inference at higher resolution can underperform low-resolution inference plus upsampling.
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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.