An enhanced combined model for water quality prediction utilizing spatiotemporal features and physical-informed constraints

Abstract

Water quality is vital for both human health and the ecological environment, and accurate predictions of the Water Quality Index (WQI) play a key role in timely monitoring of water conditions, providing essential support for environmental protection and management efforts. However, most existing studies focus on single monitoring sites, overlooking the interactions between neighboring locations. To address this limitation, this paper proposes a comprehensive water quality prediction framework that integrates spatial feature extraction, ordinary differential equations, and physical-informed constraints, called PI-GCN-SRLSTM. This framework enables WQI predictions across multiple sites and future time steps. First, a two-layer Graph Convolutional Network (GCN) is employed to capture the spatial features of WQI. Next, an enhanced Long Short-Term Memory network (LSTM), based on a second-order residual network (SRLSTM), is designed to capture complex temporal dynamics. Finally, to ensure predictions remain realistic, a gradient constraint is incorporated into the model’s loss function, improving the stability and reliability of the results. Experimental results based on the Chaohu lake dataset demonstrate that the proposed framework outperforms state-of-the-art benchmark models across six evaluation metrics: RMSE, MSE, MAE, MAPE, m1, and m2, with improvements of 30.47%, 43.04%, 29.57%, 29.92%, 0.83%, and 1.63%, respectively.