Year: 2024
Author: Janne Siipola
Communications in Computational Physics, Vol. 35 (2024), Iss. 3 : pp. 761–815
Abstract
Deep Ritz method is a deep learning paradigm to solve partial differential equations. In this article we study the generalization error of the Deep Ritz method. We focus on the quintessential problem which is the Poisson’s equation. We show that generalization error of the Deep Ritz method converges to zero with rate $\frac{C}{\sqrt{n}},$ and we discuss about the constant $C.$ Results are obtained for shallow and residual neural networks with smooth activation functions.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0253
Communications in Computational Physics, Vol. 35 (2024), Iss. 3 : pp. 761–815
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 55
Keywords: Deep learning Deep Ritz method Poisson’s equation residual neural networks shallow neural networks generalization.