Tensor Neural Network and Its Numerical Integration (Journal of Computational Mathematics, 2024)
In this paper, we introduce a type of tensor neural network. For the first time, wepropose its numerical integration scheme and prove the computational complexity to bethe polynomial scale of the dimension. Based on the tensor product structure, we develop an efficient numerical integration method by using fixed quadrature points for thefunctions of the tensor neural network. The corresponding machine learning method isalso introduced for solving high-dimensional problems. Some numerical examples are alsoprovided to validate the theoretical results and the numerical algorithm.