Improving Geothermal Heat Flow Predictions and Uncertainty Quantification using Clustering-based Quantile Regression Forests

Unsupervised clustering of geophysical data enhances supervised modeling by reducing heterogeneity in predictor variables and enabling localized, cluster-specific predictions. In this study, we apply Quantile Regression Forests (QRF), an ensemble method, to synthetic and real-world geothermal heat flow (GHF) datasets. Despite achieving strong geological and geophysical consistency in our previous continental Africa GHF model (Al-Aghbary et al., 2022), it remained an inherently ‘black-box’ model that offered limited insight into the drivers of its predictions. Moreover, that model lacked a rigorous framework for uncertainty quantification. This limitation motivated the current work, which aims to improve both interpretability and uncertainty quantification of modeling. We systematically decompose predictive uncertainty into aleatoric and epistemic components to clarify their respective contributions. The real-world application focuses on modeling GHF across continental Africa, a region characterized by geological diversity and sparse observational data. On a synthetic dataset, clustering substantially improves predictive accuracy and reliability. In the real-world dataset, performance improvements are more modest but consistent, reflecting the complexity and variability inherent to large-scale geophysical systems. Crucially, clustering reduces aleatoric uncertainty, leading to sharper and better-calibrated prediction intervals, while overall epistemic uncertainty remains nearly constant. However, in some highly heterogeneous clusters, epistemic uncertainty may increase. We compare two modeling frameworks: a Global Expert and a Mixture-of-Experts (MoE) architecture, where each cluster is assigned to a dedicated Local Expert (LE). The LE-to-cluster approach improves prediction sharpness and precision, and MoE-to-Global comparisons reveal gains in both uncertainty quantification and model interpretability. To explicitly assess our model predictions, we complement conventional accuracy, goodness-of-fit, and reliability metrics, such as root mean-squared error, coefficient of determination, and  prediction interval coverage probability, with a five-part uncertainty framework: bandwidth, variance, robustness, confidence, and explainability. These are visualized as spatial maps across the African continent. Bandwidth map reflects the narrowness (sharpness) of prediction intervals; variance map quantifies the overall spread (dispersion) of ensemble predictions; robustness map measures stability through ensemble agreement; confidence map combines sharpness and stability to highlight well-calibrated predictions intervals; and explainability map identifies the source and magnitude of uncertainty. However, this framework introduces new dependencies (e.g. clustering strategy, intra-cluster homogeneity) that could be violated in transitional regions, potentially impacting certainty in those areas. Future work should explore adaptive clustering, spatial validation to mitigate these limitations, and examine transitional areas, as the current clustering may not capture gradational changes. Overall, our QRF-based, cluster-specific MoE framework produces an uncertainty-aware, explainable model. It informs stakeholders by identifying where predictions are reliable and where improvements are needed—guiding adaptive predictor selection and targeted data collection. By distinguishing both the magnitude and source of uncertainty, the model  supports well-calibrated predictions, even in complex geophysical environments.