  We investigate the task of missing value estimation in graphs as given by
water distribution systems (WDS) based on sparse signals as a representative
machine learning challenge in the domain of critical infrastructure. The
underlying graphs have a comparably low node degree and high diameter, while
information in the graph is globally relevant, hence graph neural networks face
the challenge of long-term dependencies. We propose a specific architecture
based on message passing which displays excellent results for a number of
benchmark tasks in the WDS domain. Further, we investigate a multi-hop
variation, which requires considerably less resources and opens an avenue
towards big WDS graphs.
