A Hybrid Deep Learning Model with Spatial-Temporal Feature Fusion for Geothermal Production Prediction

Geothermal energy, a clean and reliable renewable resource, is attracting growing global attention. Predicting geothermal productivity is essential for the sustainable management of geothermal systems in conventional pumping tests, but the water level has a highly nonlinear correlation with reservoir physical conditions, and traditional numerical simulation methods fail to capture their intrinsic relationship. This study proposes a novel hybrid deep learning model of Graph Convolutional Networks (GCN) and Transformers for geothermal pumping tests, which efficiently predicts water level under nonlinear physical constraints: GCN learns the nonlinear mapping between water level depth and physical constraints, while Transformer preserves the temporal sequence correlations of production data via self-attention mechanism. Validation with test data showed that the model achieved an R2 of 0.97 and an RMSE of 0.1635 m for production wells, and an R2 of 0.94 and an RMSE of 3.9057 m for reinjection wells under different geological conditions. Its R2 showed improvements of 13.82%, 7.83%, and 5.95% compared with the LSTM, Transformer, and GCN–LSTM models, respectively. This study provides an accurate and efficient technical approach for geothermal productivity prediction, supporting the optimization of pumping test schemes and production capacity evaluation in preliminary geothermal resource development.