Physics-informed machine learning for hybrid modelling of water leakages induced by rapid valve manoeuvres in water distribution networks

Efficient leakage management in Water Distribution Networks is essential to achieving the objectives of Smart Cities and Sustainable Development Goal 6. Conventional hydraulic models based on Extended Period Simulation cannot reproduce the short transients generated by rapid valve manoeuvres, particularly in pressure-reducing and operational valves. These events create inertial effects and pressure fluctuations that strongly influence leakage behaviour, especially when valve resistance changes with real operational timings, whether manual or actuator-driven. This study develops a hybrid Physics-Informed Machine Learning framework that couples an extended Rigid Water Column Model—derived from mass and momentum conservation and incorporating time-dependent valve resistance—with supervised Machine Learning algorithms. The approach enhances leakage prediction under transient conditions by combining physical interpretability with data-driven adaptability. Simulations from the Rigid Water Column Model and Extended Period Simulation were compared across sixteen synthetic scenarios. Four optimised Machine Learning models—Fine Tree, Bagged Trees, Exponential Gaussian Process Regression, and Wide Neural Network—were trained using physically consistent datasets. They achieved Root Mean Square Error values as low as 0.0019 L per second. Tree-based algorithms proved most robust, while Exponential Gaussian Process Regression and Wide Neural Network models showed reduced extrapolation capacity. Statistical stability verified through 95 percent confidence intervals confirmed the physical coherence of predictions. The proposed framework provides a scalable and transferable tool for real-time leakage prediction and valve operation planning within Digital Twin and Supervisory Control and Data Acquisition environments, supporting predictive control, operational decision-making, and sustainable water-infrastructure management. • A PIML framework integrates RWCM physics with supervised ML for leak prediction. • Sixteen synthetic PRV closure transients are modeled using RWCM equations. • Four ML models outperform EPS, achieving R² values above 0.9999. • Generalisation is validated on unseen PRV cases using high-resolution data. • Enables real-time, scalable leakage monitoring in Digital Twins.