Prediction of geothermal heat flow for sustainable energy applications with sparse geological data using machine learning

• A machine learning framework is proposed to predict geothermal heat flow (GHF) from sparse data. • The MissForest model achieves a higher imputation accuracy than Kriging. • The XGBoost model makes accurate predictions for GHF with a low error of 10.18%. • This framework predicts GHF in unexplored regions, guiding geothermal exploitation. Geothermal heat flow (GHF) is a crucial metric in the assessment of geothermal reservoirs. To circumvent the high cost of conventional GHF measurement techniques, there is a growing interest in leveraging machine learning models to predict GHF based on geological datasets imputed by the Kriging method. However, the spatial distribution of some geological features exhibits complex data patterns and missing values, justifying the need for a more accurate and efficient alternative to the conventional Kriging method. In this study, we present a novel machine learning-based framework for predicting GHF based on sparse geological data. Specifically, a machine learning model (here MissForest) is employed to impute the missing values of geological data. The MissForest model, by leveraging spatial correlations among geological parameters (e.g., upper crust thickness, Moho depth, and rock type), achieves superior imputation accuracy (R 2 = 0.90 at 20% missing rate) over the conventional Kriging method (R 2 = 0.84). Based on the imputed datasets, machine learning regression models are trained to capture the mapping of geological features to GHF. Our best model achieves a low error of 10.18 % for predicting GHF across various regions, surpassing the previous studies. Furthermore, the machine learning-based framework successfully predicts the GHF globally, shedding new light on the distribution patterns of geothermal resources and their exploitation potential worldwide.