HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
Solving forward and inverse pde problems on unknown manifolds via physics-informed neural operators
3 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 3representative citing papers
A nested Fourier-MIONet surrogate predicts radiative heat transfer in multi-resolution 3D fire simulations with 2-4% error at reduced computational cost compared to direct RTE solves.
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
citing papers explorer
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Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
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Nested Fourier-enhanced neural operator for efficient modeling of radiation transfer in fires
A nested Fourier-MIONet surrogate predicts radiative heat transfer in multi-resolution 3D fire simulations with 2-4% error at reduced computational cost compared to direct RTE solves.
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Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.