  Detecting and localizing leakages is a significant challenge for the
efficient and sustainable management of water distribution networks (WDN).
Leveraging the inherent graph structure of WDNs, recent approaches have used
graph-based data-driven methods. However, these methods often learn shortcuts
that work well with in-distribution data but fail to generalize to
out-of-distribution data. To address this limitation and inspired by the
perfect generalization ability of classical algorithms, we propose an
algorithm-informed graph neural network (AIGNN). Recognizing that WDNs function
as flow networks, incorporating max-flow information can be beneficial for
inferring pressures. In the proposed framework, we first train AIGNN to emulate
the Ford-Fulkerson algorithm for solving max-flow problems. This algorithmic
knowledge is then transferred to address the pressure estimation problem in
WDNs. Two AIGNNs are deployed, one to reconstruct pressure based on the current
measurements, and another to predict pressure based on previous measurements.
Leakages are detected and localized by comparing the outputs of the
reconstructor and the predictor. By pretraining AIGNNs to reason like
algorithms, they are expected to extract more task-relevant and generalizable
features. Experimental results demonstrate that the proposed algorithm-informed
approach achieves superior results with better generalization ability compared
to GNNs that do not incorporate algorithmic knowledge.
