A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrödinger eigenvalue problems

This paper analyzes the generalization error of two-layer neural networks for computing ground state Schrödinger operator on add-dimensional hypercube with Neumann boundary condition. We prove that convergence rate is independent dimensiond, under a priori assumption lies in spectral Barron space. verify such by proving new regularity estimate The latter achieved fixed point argument based Krein-Rutman theorem.