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 design an efficient numerical integration method by using fixed quadrature points for the functions by the tensor neural network. The corresponding machine learning method is also introduced for solving high-dimensional eigenvalue problems. Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.

翻译：在本文中, 我们引入了一种高时神经网络。 我们第一次提出它的数字集成计划, 并证明其计算复杂性是该维度的多元尺度。 根据高时产品结构, 我们设计了一种有效的数字集成方法, 使用固定的二次点来测量高时神经网络的功能。 也引入了相应的机器学习方法来解决高维电子值问题。 还提供了一些数字示例来验证理论结果和数字算法 。