Multiscale Fourier Neural Operator
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Multiscale Fourier Neural Operator for Inverse Wave Scattering in Highly Oscillatory Media
Announce Type: new Abstract: In this paper, we propose an operator learning method based on the multiscale Fourier neural operator (MscaleFNO) for inverse medium problems of Helmholtz equations. The MscaleFNO provides a neural surrogate model with reduced spectral bias for the Helmholtz equations, mapping highly oscillatory medium profiles to scattered wavefields. A plug-and-play inversion using elucidated diffusion model is introduced to regularize the inverse solver based on least squares...
Flowers: A Warp Drive for Neural PDE Solvers
arXiv:2603.04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold, Flowers use no Fourier multipliers, no dot-product attention, and no convolutional mixing. Each head predicts a displacement field and warps the mixed input features.