Multi-scale Spatio-temporal graph neural network for enhanced water demand forecasting

Accurate Water Demand Forecasting (WDF) is essential for effectively managing the Water Distribution System (WDS). Graph neural networks, which utilize pre-defined spatial graphs to model relationships among sensor nodes, have been widely applied to WDF. Existing methods typically capture temporal dependencies at a single time scale and construct static graphs representing the most dominant spatial relationships. These limitations often impair model performance, particularly under increased graph complexity and extended forecasting horizons. To address the above issues, this study proposes a Multi-scale Spatio-Temporal Graph Neural Network (MSTGNN) tailored to the hierarchical nature of water demand time series. Specifically, MSTGNN captures multi-scale demand patterns by constructing hierarchical temporal representations ranging from fine to coarse time scales. Moreover, it adaptively learns scale-specific graph structures to reflect rich inter-sensor dependencies varying across scales. Extensive experiments on a real-world WDF dataset with 54 sensors demonstrate that MSTGNN achieves superior performance over six state-of-the-art methods in day-ahead WDF at 15-minute intervals. Its strength in modeling multi-scale spatio-temporal dependencies significantly enhances forecasting accuracy and scalability, supporting advanced smart applications in WDS.