HG-PINN: A residual physics-informed neural network framework for heterogeneous groundwater flow simulation

Accurately modeling groundwater flow in heterogeneous aquifers remains challenging due to spatial variability and boundary complexity. Physics-informed neural networks (PINNs) have shown advantages in groundwater flow modeling by embedding physical priors into deep learning frameworks. However, conventional PINNs often suffer from slow convergence and limited precision when applied to highly non-uniform hydrogeological settings. To overcome the aforementioned limitations, this study presents an enhanced framework incorporating a heterogeneity-guided mechanism, referred to as HG-PINN. This method integrates modular residual structures, parameter-supervised learning, and hard constraint embedding mechanisms. Several pumping cases are applied to validate the proposed model and the calculations are compared to the numerical simulation. The results demonstrate that HG-PINN can simulate the groundwater flow effectively when pumping in both homogeneous and heterogeneous aquifers. In addition, ablation studies were conducted to investigate the effects of network depth, activation functions, and model structure on performance. Appropriate network deepening and the use of hyperbolic tangent activation were found to improve convergence and accuracy. Relative to traditional PINNs, HG-PINN further reduces errors and enhances boundary representation in heterogeneous aquifers. This method integrates the strengths of data-driven learning and physical constraints, offering a new approach for high-precision groundwater flow simulation with broad engineering application potential.