A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems

05/04/2021 ∙ by Jianfeng Lu, et al. ∙ 0

This paper analyzes the generalization error of two-layer neural networks for computing the ground state of the Schrödinger 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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