Year: 2024
Type: preprint
Abstract: In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality reduction technique, and then calculate the Galerkin projection of the eigenvalue problem onto the subspace spanned by the orthogonal basis and obtain an approximate solution. Numerical experiments show that we can obtain approximate eigenvalues and eigenfunctions with very high accuracy but low cost.
Source: arXiv (Cornell University)
Authors: Dai, Xiaoying, Fan, Yunying, Sheng, Zhiqiang
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403579522