Improvements in groundwater level prediction using a graph data assimilation–based physics-informed neural network (Handan City, China)

Study region: This study focuses on Guantao County in Handan City, Hebei Province, China, which is located within an area of groundwater overexploitation on the North China Plain. Study focus: Groundwater-level prediction is of great importance for mitigating groundwater overexploitation and managing regional water resources. However, most conventional deep-learning approaches are data-driven and lack explicit representations of multi-well hydraulic connections and groundwater-dynamics constraints, leading to limited generalization and insufficient physical consistency under complex recharge–pumping conditions. To address this issue, this study presents a physics-informed neural network integrating graph data assimilation and a discrete physical updating mechanism (PINN-GDA). Using a “sequence encoding–graph propagation–physical update–target regression” architecture, multi-well observed groundwater levels, meteorological drivers, and extraction volume were jointly incorporated into a unified deep-network framework. New hydrological insights: The comprehensive results showed that, relative to the baseline and ablation models, the PINN-GDA model reduced RMSE by 23.5%, 36.2%, 22.1%, and 20.2%, respectively, and decreased Bias by 92.1%, 93.3%, 88.1%, and 87.5%. Moreover, across low-, medium-, and high-water-level stages, consistently lower median errors and stronger stability were maintained by PINN-GDA, and the performance gains were mainly attributed to the synergistic effects of the physical constraints and the graph assimilation mechanism. These findings underscore that higher predictive accuracy was achieved by PINN-GDA through coupling groundwater-dynamics-inspired, physics-guided regularization with the inter-well spatial structure. • A physics-informed neural network integrating graph data assimilation and a discrete physical updating mechanism (PINN-GDA) is proposed. • The PINN-GDA model couples groundwater-dynamics-inspired, physics-guided regularization with the inter-well spatial structure. • A unified multi-module, multi-source architecture of “temporal encoding–graph propagation–physical updating–target regression” is constructed. • The PINN-GDA model explicitly accounts for multi-well interactions and provides a conceptual bridge between purely data-driven prediction and physics-driven groundwater dynamics.