PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations

被引:8
|
作者
Sheng, Hailong [1 ,3 ]
Yang, Chao [2 ,4 ]
机构
[1] Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[3] Univ Chinese Acad Sci, Beijing 100190, Peoples R China
[4] Peking Univ, Inst Comp & Digital Econ, Changsha 410205, Peoples R China
基金
中国国家自然科学基金;
关键词
Neural network; penalty-free method; domain decomposition; initial-boundary value problem; partial differential equation; DEEP LEARNING FRAMEWORK; BOUNDARY-VALUE-PROBLEMS; RITZ METHOD; ALGORITHM;
D O I
10.4208/cicp.OA-2022-0114
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the smoothness constraints and essential boundary conditions of self-adjoint problems with complex geometries, and extends the application to a broader range of non-self-adjoint time-dependent differential equations. In addition, PFNN-2 introduces an overlapping domain decomposition strategy to substantially improve the training efficiency without sacrificing accuracy. Experiments results on a series of partial differential equations are reported, which demonstrate that PFNN-2 can outperform state-of-the-art neural network methods in various aspects such as numerical accuracy, convergence speed, and parallel scalability.
引用
收藏
页码:980 / 1006
页数:27
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