Abstract
Water distribution systems (WDS) face complex challenges, including real-time monitoring, operational efficiency, and resilience under varying hydraulic conditions. Artificial intelligence (AI) offers promising solutions but is often held back by its lack of transparency. This paper presents a novel framework integrating Explainable AI (XAI) with graph signal processing to enhance the interpretability of AI models applied to WDS. Specifically, it models multilayer perceptrons as dynamic, weighted, directed graphs to analyse hydraulic states. Using eigencentrality as a central graph metric, this approach identifies key drivers influencing model predictions, offering insights into both global and local system behaviour. The methodology is validated using a metamodel for hydraulic state estimation, leveraging real-world WDS benchmarks. Comparative analyses with state-of-the-art XAI approaches, such as the SHapley Additive exPlanations (SHAP values) and Integrated Gradients (IG), demonstrate the robustness, adaptability, and computational efficiency of the proposed novel framework, with processing times that are over 70 times faster. This enables real-time applications in digital twins for WDS. Moreover, the methodology supports sensor prioritization and maintenance strategies, emphasizing critical components for system resilience. The results highlight the synergy between graph theory and XAI, showcasing a scalable, transparent tool for sustainable urban water management.