Speaker：Hehu Xie（Chinese Academy of Sciences）

Time：2022-12-06, 09:00

Location：Tencent Meeting ID：274-251-012（No Password）

Abstract:

This report will introduce a numerical discretization method based on tensor decomposition for solving partial differential equations. Based on this idea, a tensor neural network and its corresponding machine learning algorithm are introduced. The neural grid is built based on the form of tensor product, which can directly integrate high-dimensional functions, and convert high-dimensional integrals with exponential complexity into polynomial tensor integrals without the help of Monte Carlo process. Next, we use tensor neural network to design machine learning algorithms for solving high-dimensional partial differential equations and eigenvalue problems, hoping to bring more degrees of freedom and operability to the solution of high-dimensional partial differential equations. The application of tensor discrete method and machine learning algorithm of tensor neural network in solving high-dimensional eigenvalue problems and multibody problems will be introduced in the report.