Integrating physics-based constraints with gated recurrent unit for improved groundwater level fluctuation prediction

This study presents a physics-informed neural network (PINN) that integrates the linear ordinary differential equation of hydrodynamics within a Gated Recurrent Unit (GRU) network. By embedding physics-based constraints within a data-driven framework, the proposed model effectively incorporates hydrological principles and historical data patterns, enhancing both the predictive accuracy and physical consistency of groundwater level (GL) predictions. The model's performance was evaluated using six years (2005–2010) of daily GL and precipitation data collected from six monitoring wells across South Korea, selected to represent diverse hydrogeological conditions. Comparative analyses against a purely data-driven GRU model and a physics-based linear reservoir model demonstrate that the PINN framework consistently outperforms both approaches across key predictive metrics, including root mean squared error (RMSE), correlation coefficient (CC), and Nash-Sutcliffe efficiency (NSE). Compared to the GRU-based model, the proposed PINN-based model exhibited significantly enhanced performance, reducing RMSE by up to 55.9%, improving CC by 37.1%, and increasing NSE from 0.02 to 0.87. Notably, the PINN model maintains superior accuracy even when trained on lower temporal resolution datasets. The study reveals that incorporating even simplified physical constraints significantly improves the generalization capability of data-driven models, mitigating overfitting and enabling more reliable predictions under real-world hydrological conditions. Furthermore, the PINN model effectively captured GL fluctuation patterns that a purely physics-based model struggled to represent, particularly those arising from localized hydrogeological heterogeneity and site-specific aquifer dynamics. These findings underscore the practical value of PINNs as a robust and physically consistent solution for GL modeling, particularly in data-scarce or noise-prone environments.