A Novel Transfer Learning-Based Adaptive Weight Physics-Informed Neural Network for Groundwater Modeling in the Middle Reaches of Heihe River Basin, Northwestern China

Accurate groundwater modeling is paramount for ensuring the stability and sustainability of water resources, especially in the arid and semi-arid regions. Traditional numerical models are compute-intensive, while data-driven models are constrained by training data quality, lacking physical consistency. Although Physics-Informed Neural Networks (PINNs) incorporate physical laws, their fixed loss function weights struggle to balance gradients among constraints, limiting optimization stability and convergence. In this paper, the Transfer Learning-based Adaptive-Weighting Physics-Informed Neural Network (TL-AWPINN) is proposed to simulate groundwater dynamics in the middle reaches of the Heihe River basin, northwestern China. First, building upon a loss function derived from the governing differential equation for groundwater flow, this model introduces an adaptive weighting method. This method intensifies the penalty on unsatisfied physical constraints during training, enabling more effective simulation of dynamic behavior. Second, the TL-AWPINN model is pre-trained using a 2D heterogeneous unconfined aquifer scenario S and gridded data from the Heihe River Basin, with target data from MODFLOW simulations. Subsequently, this pre-trained model is fine-tuned using a limited set of real-world observation data, adapting prior knowledge from the numerical model to field conditions. Experimental results show the TL-AWPINN model achieves MAE = 0.13688 m, RMSE = 0.18785 m, and R² = 0.96460 against MODFLOW data in the middle reaches of the Heihe River Basin. After fine-tuning, it accurately predicts groundwater level trends, validating reliability and effectiveness.