TY - JOUR
T1 - Tensor Neural Network and Its Numerical Integration
AU - Wang , Yifan
AU - Xie , Hehu
AU - Jin , Pengzhan
JO - Journal of Computational Mathematics
VL - 6
SP - 1714
EP - 1742
PY - 2024
DA - 2024/11
SN - 42
DO - http://doi.org/10.4208/jcm.2307-m2022-0233
UR - https://global-sci.org/intro/article_detail/jcm/23513.html
KW - Tensor neural network, Numerical integration, Fixed quadrature points, Machine learning, High-dimensional eigenvalue problem.
AB - <p style="text-align: justify;">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.</p>