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This work proves existence, uniqueness, and maximal regularity with a gain of one derivative in time and $\gamma$ derivatives in space, where $\gamma>0$ is the order of the fractional Laplacian.
We establish a dimension-efficient neural network approximation theory for solutions to fractional parabolic equations with lower-order drift and potential terms. By introducing anisotropic spectral Barron spaces, which measure temporal and spatial regularity separately in frequency space, we first develop a dimension-...
Localized extreme precipitation is a major trigger of urban flash floods and landslides, yet producing nowcasts that combine fine spatial detail with probabilistic uncertainty remains challenging. Here we introduce exPreCast-ENS, a conditional residual diffusion framework that transforms the deterministic 4 km radar no...
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