论文标题
PFNN-2：用于解决部分微分方程的域分解无惩罚神经网络方法
PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations
论文作者
论文摘要
提出了一种新的无惩罚神经网络方法PFNN-2，用于解决部分微分方程，这是我们先前提出的PFNN方法的随后改进[1]。 PFNN-2继承了PFNN的所有优势，在处理具有复杂几何形状的自我接合问题问题的平滑度约束和基本边界条件中，并将应用扩展到更广泛的非自动参与时间依赖时间依赖的微分方程。此外，PFNN-2还引入了重叠的域分解策略，以实质上提高训练效率而不牺牲准确性。报告了一系列偏微分方程的实验结果，这些方程报告表明，PFNN-2可以在各个方面（例如数值准确性，收敛速度和并行的可伸缩性）胜过最先进的神经网络方法。
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.
