Hierarchical physics-informed neural networks for water contamination prediction in water distribution systems: integrating physics-based modeling and AI transfer learning

Water distribution systems (WDSs) are at risk of contamination, requiring accurate real-time monitoring. This study presents the hierarchical physics-informed neural network (HPINN) for water contamination detection. It combines a global physics-informed neural network (PINN) for general contaminant dynamics and pipe-specific transfer learning for localized predictions. A sliding-window calibration further enhances real-time sensitivity. Tested on a 40-pipe, 35-node network, the model achieved a mean absolute percentage error (MAPE) of 0.24% for training and 0.31% for testing, outperforming traditional models (backpropagation neural networks (BP): 1.27%, support vector machines (SVM): 0.69%, long short-term memory (LSTM): 0.68%). HPINN also maintained an F1 score of 1.00 under 45 sensor failure scenarios, demonstrating robustness. This model provides a scalable, effective solution for contamination detection, reducing reliance on extensive sensor infrastructure and improving fault tolerance, making it ideal for regions with limited resources.