Graph neural networks to model and optimize the operation of water distribution networks. A review

Water Distribution Networks (WDNs) have become increasingly complex and interconnected, and the need for advanced modeling and optimization techniques has become fundamental to ensure an efficient and reliable clean water supply. Representing WDNs as graphs naturally models the underlying interacting physical structure and enables the usage of Graph Neural Networks (GNN) that combine the physical structure with abstract notions to capture local and global relationships. GNNs offer significant advantages in contrast to generic Deep Learning (DL) techniques and stand out as a promising solution to model intricate dependencies and enable the investigation of key challenges such as leak detection, water quality monitoring, and demand forecasting. This review presents the physics and hydraulics involved in WDN and the prevalent graph-based models used in the literature. The theoretical foundations of GNNs are shown, highlighting their capabilities in capturing complex spatial relationships and dependencies inherent in the network topology. The most promising GNN-based solutions that can address some of the most critical challenges of WDNs are discussed in detail. We outline the open challenges and potential directions for future developments in this field. By combining multidisciplinary and real-world aspects, this critical review highlights the role of GNNs in modeling and optimizing WDNs.