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.

翻译：为提高神经网络逼近偏微分方程的解精度和训练效率，可采用分区神经网络作为解替代模型，而非在整个问题域上定义单个大型深度神经网络。在这种分区神经网络方法中，需结合适当的界面条件或子域边界条件以获得收敛的近似解。然而，目前尚未对分区神经网络方法的收敛性及并行计算性能提升进行严格研究。本文针对上述问题提出了迭代算法。该算法基于经典加性施瓦茨区域分解方法。文中给出了数值结果，以展示所提迭代算法的性能。