FreqNO-DPS corrects neural operator spectral bias in 3D elastic wavefield prediction by frequency-dependent guidance in diffusion posterior sampling conditioned on sparse observations, achieving near-zero bias at 2-5% sensor coverage.
Mscalefno: Multi-scale fourier neural operator learning for oscillatory function spaces.arXiv preprint arXiv:2412.20183
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GSNO uses position-dependent spherical Green's functions to create flexible neural operators that adapt to non-equivariant systems on spheres while keeping spectral efficiency and grid invariance.
An approximate greedy router for hybrid PDE solvers that mimics optimal selection without true error access and shows faster, more stable error reduction on test equations.
citing papers explorer
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Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
FreqNO-DPS corrects neural operator spectral bias in 3D elastic wavefield prediction by frequency-dependent guidance in diffusion posterior sampling conditioned on sparse observations, achieving near-zero bias at 2-5% sensor coverage.
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Generalized Spherical Neural Operators: Green's Function Formulation
GSNO uses position-dependent spherical Green's functions to create flexible neural operators that adapt to non-equivariant systems on spheres while keeping spectral efficiency and grid invariance.
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A Greedy PDE Router for Blending Neural Operators and Classical Methods
An approximate greedy router for hybrid PDE solvers that mimics optimal selection without true error access and shows faster, more stable error reduction on test equations.