Year: 2024
Author: Yifan Wang, Hehu Xie, Pengzhan Jin
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1714–1742
Abstract
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product structure, we develop an efficient numerical integration method by using fixed quadrature points for the functions of the tensor neural network. The corresponding machine learning method is also introduced for solving high-dimensional problems. Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2307-m2022-0233
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1714–1742
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Tensor neural network Numerical integration Fixed quadrature points Machine learning High-dimensional eigenvalue problem.
Author Details
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