Surrogate Modeling for Geothermal Hydraulic Field Based on Physics-informed Neural Networks

Geothermal energy is renewable resource with sustainable development potential, utilizing artificial intelligence algorithms for geothermal resource extraction has become an inevitable development trend. Traditional machine learning methods for predicting geothermal production suffer from low computational efficiency and poor transferability. Therefore, a two-dimensional surrogate model for geothermal hydraulic field based on a Physics-Informed Neural Networks (PINN) has been established. The two-dimensional flow equations and reservoir parameters were embedded as constraints within the neural network to predict the pressure distribution after 10 years of production. The neural network was optimized by minimizing the loss function, and the pressure field predicted by the trained surrogate model was compared with results from numerical simulation for validation and analysis. The results indicate that the Physics-Informed Neural Networks can learn a surrogate model with stronger generalization capabilities using fewer data samples. The trained model achieved an average absolute error (MAE) of 0.09, an average absolute percentage error (MAPE) of 0.19%, demonstrating superior prediction performance that aligns more closely with field conditions. In the future, the method is expected to enable further exploration and applications in geothermal multi-physical field coupling.