  Domain decomposition methods are widely used and effective in the
approximation of solutions to partial differential equations. Yet the optimal
construction of these methods requires tedious analysis and is often available
only in simplified, structured-grid settings, limiting their use for more
complex problems. In this work, we generalize optimized Schwarz domain
decomposition methods to unstructured-grid problems, using Graph Convolutional
Neural Networks (GCNNs) and unsupervised learning to learn optimal
modifications at subdomain interfaces. A key ingredient in our approach is an
improved loss function, enabling effective training on relatively small
problems, but robust performance on arbitrarily large problems, with
computational cost linear in problem size. The performance of the learned
linear solvers is compared with both classical and optimized domain
decomposition algorithms, for both structured- and unstructured-grid problems.
