English(EN) Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces

新研究探讨谱Barron空间中的偏微分方程正则性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-07 04:00

一篇新发表在arXiv上的研究论文详细介绍了在谱Barron空间中二阶椭圆偏微分方程（PDE）的正则性定理。研究表明，在特定的椭圆性和小性条件下，解可以获得两个额外的Barron正则性阶数。这项工作的一个关键启示是识别了一类PDE，其解可以通过利用余弦激活函数的两层神经网络来逼近，并且网络宽度与空间维度无关。 AI

影响这项研究可能能够更有效地逼近某些类型的偏微分方程的神经网络。

排序理由该集群包含一篇关于arXiv的学术论文，详细介绍了数学研究。[lever_c_demoted from research: ic=1 ai=0.7]

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arXiv cs.LG TIER_1 English(EN) · Ziang Chen, Liqiang Huang, Mengxuan Yang, Shengxuan Zhou · 2026-09-07 04:00

谱Barron空间中二阶椭圆偏微分方程的正则性

arXiv:2602.19381v2 Announce Type: replace-cross Abstract: We establish a regularity theorem for second-order elliptic PDEs on $\mathbb{R}^{d}$ in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains two additional orders of Barron regularit…

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谱Barron空间中二阶椭圆偏微分方程的正则性

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