In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of trial function for the high dimensional partial differential equations. Based on the tensor structure of the trial functions, we can do the direct numerical integration of the approximate solution without the help of Monte-Carlo method. Then combined with the Ritz or Galerkin method, solving the high dimensional partial differential equation can be transformed to solve a concerned optimization problem. Some numerical tests are provided to validate the proposed numerical methods.

翻译：在本文中,我们建议了解决高维部分差异方程式的强分解和优化程序。 首先,我们设计了高维部分差异方程式的强分函数。根据审判功能的强分结构,我们可以在不借助蒙特-卡洛方法的情况下,直接将近似解决方案数字整合在一起。然后,与里兹或加勒金方法相结合,解决高维部分差异方程式可以转换为解决相关的优化问题。提供了一些数字测试,以验证拟议的数字方法。