Author

Hyojae Lim

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Preprint Jul 2026

Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation

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.

Jae-Hwan Choi, Hyojae Lim, Jinsol Seo et al. · 1 citation

Jul 2026

Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations

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-...

Jae-Hwan Choi, Hyojae Lim, Jinsol Seo et al. · arXiv.org · 2 citations