  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.
