PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations
Year: 2022
Author: Hailong Sheng, Chao Yang
Communications in Computational Physics, Vol. 32 (2022), Iss. 4 : pp. 980–1006
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0114
Communications in Computational Physics, Vol. 32 (2022), Iss. 4 : pp. 980–1006
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Neural network penalty-free method domain decomposition initial-boundary value problem partial differential equation.