A Data Assimilation Methodology to Analyze the Unsaturated Seepage of an Earth–Rockfill Dam Using Physics-Informed Neural Networks Based on Hybrid Constraints

Data assimilation for unconfined seepage analysis has faced significant challenges due to hybrid causes, such as sparse measurements, heterogeneity of porous media, and computationally expensive forward models. To address these bottlenecks, this paper introduces a physics-informed neural network (PINN) model to resolve the data assimilation problem for seepage analysis of unsaturated earth–rockfill dams. This strategy offers a solution that decreases the reliance on numerical models and enables an accurate and efficient prediction of seepage parameters for complex models in the case of sparse observational data. For the first attempt in this study, the observed values are obtained by random sampling of numerical solutions, which are then contributed to the synchronous constraints in the loss function by informing both the seepage control equations and boundary conditions. To minimize the effects of sharp gradient shifts in seepage parameters within the research domain, a residual adaptive refinement (RAR) constraint is introduced to strategically allocate training points around positions with significant residuals in partial differential equations (PDEs), which could facilitate enhancing the prediction accuracy. The model’s effectiveness and precision are evaluated by analyzing the proposed strategy against the numerical solutions. The results indicate that even with limited sparse data, the PINN model has great potential to predict seepage data and identify complex structures and anomalies inside the dam. By incorporating coupling constraints, the validity of our PINN model could lead to theoretically viable applications of hydrogeophysical inversion or multi-parameter seepage inversion. The results show that the proposed framework can predict the seepage parameters for the entire research domain with only a small amount of observation data. Furthermore, with a small amount of observation data, PINNs are able to obtain more accurate results than purely data-driven DNNs.