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Title: 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 the ground state of the Schrödinger 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.
Award ID(s):
2107934 2012286
Publication Date:
Journal Name:
Communications of the American Mathematical Society
Page Range or eLocation-ID:
1 to 21
Sponsoring Org:
National Science Foundation
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