  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.
