Hybrid FEM–PINN framework for seepage prediction in zoned earth dams: a case study of Eyvashan dam

Seepage is a critical factor influencing the long-term safety of zoned earth dams. This study presents a hybrid data–physics framework integrating a calibrated Finite Element Method (FEM) with a Physics-Informed Neural Network (PINN) to enhance seepage prediction while maintaining physical consistency. The transient groundwater flow equation is directly embedded into the loss function via automatic differentiation. Training utilized eight years of monitoring records (1,118 samples) from Eyvashan Dam (Iran) combined with FEM synthetic data in a 60:40 ratio, using a strict chronological data split. Benchmarked against Random Forest (RF) and Extreme Gradient Boosting (XGBoost), the proposed PINN achieved superior predictive precision ( \(\:{R}²=0.992\) , \(\:RMSE=0.018\:L/s\) , and \(\:MAE=0.013\:L/s\) ), outperforming XGBoost ( \(\:{R}²=0.975\) ) and RF ( \(\:{R}²=0.941\) ). Stochastic Monte Carlo uncertainty analysis demonstrated that PINN preserved the narrowest 95% prediction interval ( \(\:95%\:PI=[-0.004,0.028]{\:m}³/s\) ) and lowest variance ( \(\:σ\:=0.008\:L/s\) ). Explainable artificial intelligence (XAI) confirmed reservoir level and core hydraulic conductivity as dominant factors, adhering to Darcy’s law. A standalone Graphical User Interface (GUI) was developed, establishing a robust offline digital twin prototype for intelligent dam safety monitoring.