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arXiv · 2105.01228

A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schr\"odinger Eigenvalue Problems

Jianfeng Lu·Yulong Lu
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Abstract

This paper analyzes the generalization error of two-layer neural networks for computing the ground state of the Schr\"odinger operator on a $d$-dimensional hypercube. We prove that the convergence rate of the generalization error is independent of the dimension $d$, under the a priori assumption that the ground state lies in a spectral Barron space. We verify such assumption by proving a new regularity estimate for the ground state in the spectral Barron space. The later is achieved by a fixed point argument based on the Krein-Rutman theorem.

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BibTeXRIS

Jianfeng Lu, Yulong Lu. 2021-05-04. A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schr\"odinger Eigenvalue Problems. https://arxiv.org/abs/2105.01228

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