TY - JOUR
T1 - PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations
AU - Sheng , Hailong
AU - Yang , Chao
JO - Communications in Computational Physics
VL - 4
SP - 980
EP - 1006
PY - 2022
DA - 2022/10
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2022-0114
UR - https://global-sci.org/intro/article_detail/cicp/21136.html
KW - Neural network, penalty-free method, domain decomposition, initial-boundary value problem, partial differential equation.
AB - <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>