论文标题
张量神经网络及其数值集成
Tensor Neural Network and Its Numerical Integration
论文作者
论文摘要
在本文中，我们引入了一种张量神经网络。我们第一次提出其数值集成方案，并证明计算复杂性是维度的多项式尺度。基于张量产品结构，我们通过使用张量神经网络功能的固定正交点来开发有效的数值集成方法。还引入了相应的机器学习方法来解决高维问题。还提供了一些数值示例来验证理论结果和数值算法。
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.
