A physics-constrained spatio-temporal deep learning model for water depth prediction in urban drainage systems

Under climate change, urban flooding has become increasingly severe and its early warning is of significance. This study developed a physics-constrained spatio-temporal deep learning model based on a Graph Neural Network (GNN) and a Long Short-Term Memory (LSTM) network, namely, the Phy-STNN model. The model incorporated both the spatial topology of drainage systems and the temporal variation of hydraulic parameters to predict the water depth in drainage systems. It also included the flow balance in the pipe network as a physics constraint. Additionally, the spatio-temporal Moran's I, which was created by adding the temporal terms into the conventional Moran's I, was applied to evaluate the performance of the Phy-STNN model in capturing spatio-temporal features. The Phy-STNN model was validated with the drainage network in China's city Shenzhen, which exhibited a significantly improved prediction accuracy compared to GNN or LSTM models, with R2 values above 0.95 for the prediction of water depth in each manhole. The Phy-STNN model can effectively capture the spatio-temporal dynamic features of urban flooding with low computational cost. It can contribute to early warning and efficient management of urban flooding.