Tensor Neural Network and Its Numerical Integration

Understand

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.