Physics-informed spatiotemporal graph neural network models for groundwater contaminant prediction

Groundwater contamination prediction is challenging because of the strong concealment, complex spatiotemporal coupling, and high parameter dependence of physical mechanism models. However, traditional data-driven models lack spatial representations. To address these limitations, this study developed and compared three physics-driven spatiotemporal graph neural network (STGNN) architectures for groundwater contamination prediction: a recurrent model (RGNN-ST), a convolutional model (ConvGNN-ST), and an attention-based model (AttentionGNN-ST). A dynamic graph construction strategy was designed to embed hydraulic head and hydraulic conductivity into edge weights, thereby linking data-driven learning to Darcy-flow constraints. Training and testing datasets were generated using coupled MODFLOW-MT3DMS simulations of homogeneous and heterogeneous aquifers. The model performance was evaluated in terms of prediction accuracy, computational efficiency, robustness, and interpretability of the results. The results indicate that RGNN-ST provided the most reliable overall performance: under homogeneous conditions, R² reached 99.95% and NRMSE was 1.68%; under heterogeneous conditions,the average R² was 99.60%. RGNN-ST also exhibited the strongest stability and the best accuracy-efficiency balance across monitoring configurations. All models exhibited good robustness to monitoring node density, time window length, and aquifer heterogeneity, and accurately captured the spatiotemporal migration patterns of contaminants. Interpretability analysis revealed that RGNN-ST balances multi-source physical features (concentration, hydraulic head, hydraulic conductivity), automatically identifies key monitoring nodes and critical time steps, and its prediction behavior conforms to the physical mechanism of groundwater movement. The proposed physics-informed STGNN framework provides a transferable modeling strategy for groundwater contamination forecasting, risk management, and monitoring-network optimization.