论文标题
分区神经网络近似与部分微分方程的迭代算法
Iterative algorithms for partitioned neural network approximation to partial differential equations
论文作者
论文摘要
为了增强对部分微分方程的神经网络近似的解决方案准确性和训练效率，可以将分区的神经网络用作解决方案替代物，而不是整个问题域上定义的单个大型神经网络。在这种分区的神经网络方法中，合并的界面条件或子域边界条件合并以获得收敛的近似解决方案。但是，没有关于分区神经网络方法的收敛和平行计算增强的严格研究。在本文中，提出了迭代算法来解决这些问题。我们的算法基于经典的施加兹域分解方法。包括数值结果以显示所提出的迭代算法的性能。
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain a convergent approximate solution. However, there has been no rigorous study on the convergence and parallel computing enhancement on the partitioned neural network approach. In this paper, iterative algorithms are proposed to address these issues. Our algorithms are based on classical additive Schwarz domain decomposition methods. Numerical results are included to show the performance of the proposed iterative algorithms.
