%ALu, Jianfeng%ALu, Yulong%BJournal Name: Communications of the American Mathematical Society; Journal Volume: 2; Journal Issue: 1
%D2022%I
%JJournal Name: Communications of the American Mathematical Society; Journal Volume: 2; Journal Issue: 1
%K
%MOSTI ID: 10324294
%PMedium: X; Size: 1 to 21
%TA priori generalization error analysis of two-layer neural networks for solving high dimensional SchrÃ¶dinger eigenvalue problems
%XThis paper analyzes the generalization error of two-layer neural networks for computing the ground state of the SchrÃ¶dinger operator on a d d -dimensional hypercube with Neumann boundary condition. We prove that the convergence rate of the generalization error is independent of dimension d 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 latter is achieved by a fixed point argument based on the Krein-Rutman theorem.
%0Journal Article