Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions
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Abstract (arXiv)
We study the complexity of approximating high-dimensional second-order elliptic PDEs with homogeneous boundary conditions on the unit hypercube using Barron spaces. Under suitable Barron assumptions on the coefficients and forcing term, we prove that the solutions can be approximated to any prescribed accuracy (varepsilon>0) by two-layer neural networks whose widths and relevant parameters are bounded by (Obigl(dC|logvarepsilon|bigr)). Consequently, we identify a class of elliptic PDEs that can be approximated by shallow neural networks without suffering from the curse of dimensionality.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 26 of its 58 references that are in the map. First posted on arXiv 11 Aug 2025.
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14 more
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