Multi-scale time series decomposition for water demand forecasting based on LSTM_Mixer

Reliable water demand forecasting models are crucial to support water utilities in optimizing the operational schedules of water supply systems. Machine learning (ML)-based implicit models have been widely used in this domain. However, most ML-based models often function as “black boxes” without interpretability. This study proposes a deep learning model, Long Short-Term Memory Mixer (LSTM_Mixer), for urban water demand forecasting based on multi-scale time series decomposition. The model decomposes water demand data into three temporal components, namely the weekly, daily, and hourly components, during the model training process. This decomposition-integration framework inherently enhances model interpretability and enables the explicit analysis of the patterns of different temporal components and their contribution to the overall prediction, thus providing insights into underlying water demand patterns. The model is validated through application on ten District Metered Areas (DMAs) with diverse characteristics, demonstrating its superior performance in 1-step, 24-step, and 168-step water demand forecasting scenarios. Comparisons with six existing deep learning models show that the LSTM_Mixer model achieved the best performance in 72.5%, 70%, and 40% of the indicators. Moreover, the LSTM_Mixer model significantly improves interpretability by presenting the multi-scale decomposition process explicitly, offering a reliable solution for water demand forecasting.