A physics-guided clustered GBRT ensemble model for geothermal heat flow prediction and its application in China

Abstract Geothermal heat flow (GHF) is essential for quantifying lithospheric thermal conditions and supporting geothermal resource assessment. However, direct GHF measurements remain sparse and unevenly distributed due to drilling limitations and high acquisition costs. While machine learning offers a scalable alternative for GHF estimation, purely data-driven models often struggle to capture complex geological heterogeneity, and their performance tends to plateau as additional geophysical features are introduced. This study introduces a physics-guided clustered Gradient Boosting Regression Trees (GBRT) ensemble framework. Nineteen geological and geophysical features were incorporated, including two newly developed analytical GHF features derived from thermal equilibrium and conduction principles as physics-derived features. The clustered ensemble method significantly enhances prediction accuracy compared with a baseline GBRT model. Ensemble performance plateaus at eight model units, yielding an R 2 of 92.01% and reductions in MAE and RMSE of 22.72% and 22.37%, respectively. The analytical features show the highest importance scores, demonstrating that embedding physics-guided constraints improves interpretability and reliability. Finally, an updated GHF map of China is generated, offering improved alignment with geothermal manifestations such as high-temperature springs. The proposed framework advances the use of ensemble and physics-guided learning for robust GHF estimation in data-scarce regions.