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Research questionWhen do second-order elliptic PDE solutions gain two orders of spectral Barron regularity for dimension-independent neural-network approximation?For elliptic PDEs on \(\mathbb{R}^d\), approximation depends on whether solution regularity can be strengthened in a dimension-robust way. The key issue is how spectral Barron regularity relates to the width required by neural networks.
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Research Paper
Latest papersRecent research connected to this question, newest first.Regularity of Second-Order Elliptic PDEs in Spectral Barron SpacesThe result concerns second-order elliptic PDEs in spectral Barron spaces under mild ellipticity and smallness assumptions. It supplies evidence for a two-order regularity gain and a corollary covering two-layer cosine networks with width independent of spatial dimension.research paper · Sep 3, 2026
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