@Article{CiCP-32-4,
author = {Sheng, Hailong and Yang, Chao},
title = {PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations},
journal = {Communications in Computational Physics},
year = {2022},
volume = {32},
number = {4},
pages = {980--1006},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0114},
url = {https://global-sci.com/article/79488/pfnn-2-a-domain-decomposed-penalty-free-neural-network-method-for-solving-partial-differential-equations}
}