TENSOR NEURAL NETWORK AND ITS NUMERICAL INTEGRATION  

作　　者：Yifan Wang Hehu Xie Pengzhan Jin 

机构地区：[1]LSEC,NCMIS,Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [3]School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Journal of Computational Mathematics》2024年第6期1714-1742,共29页计算数学（英文）

基　　金：supported in part by the National Key Research and Development Program of China(Grant No.2019YFA0709601);by the National Center for Mathematics and Interdisciplinary Science,CAS.

摘　　要：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.

关 键 词：Tensor neural network Numerical integration Fixed quadrature points Machine learning High-dimensional eigenvalue problem 

分 类 号：O17[理学—数学]