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

Improving Geothermal Heat Flow Predictions and Uncertainty Quantification using Clustering-based Quantile Regression Forests | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 28 July 2025 V1 Latest version Share on Improving Geothermal Heat Flow Predictions and Uncertainty Quantification using Clustering-based Quantile Regression Forests Authors : Magued Al-Aghbary 0000-0002-8033-3846 [email protected] , Mohamed Osman Awaleh , Mohamed Jalludin , Mohamed Sobh 0000-0003-1769-7353 , Christian Gerhards 0000-0003-2417-5377 , Tobias Staal 0000-0002-4323-6748 , Mohamed Sobh , Tobias Stål , and Christian Gerhards Authors Info & Affiliations https://doi.org/10.22541/au.175373261.14525669/v1 387 views 273 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 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. Supplementary Material File (preprint_improving geothermal heat flow predictions and uncertainty quantification using clustering-based quantile regression forests1.pdf) Download 6.39 MB File (preprint_supportive_information_improving geothermal heat flow predictions and uncertainty quantification using clustering-based quantile regression forests.pdf) Download 21.33 MB Information & Authors Information Version history V1 Version 1 28 July 2025 Copyright This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License Keywords africa geothermal heat flow machine learning Authors Affiliations Magued Al-Aghbary 0000-0002-8033-3846 [email protected] Institute of Geophysics and Geoinformatics, TU Bergakademie Freiberg Institut des Sciences de la Terre, Centre d'Etudes et de Recherches de Djibouti (CERD) View all articles by this author Mohamed Osman Awaleh Institut des Sciences de la Terre, Centre d'Etudes et de Recherches de Djibouti (CERD) View all articles by this author Mohamed Jalludin Institut des Sciences de la Terre, Centre d'Etudes et de Recherches de Djibouti (CERD) View all articles by this author Mohamed Sobh 0000-0003-1769-7353 View all articles by this author Christian Gerhards 0000-0003-2417-5377 View all articles by this author Tobias Staal 0000-0002-4323-6748 View all articles by this author Mohamed Sobh Leibniz Institute for Applied Geophysics (LIAG) View all articles by this author Tobias Stål School of Natural Sciences (Physics), University of Tasmania View all articles by this author Christian Gerhards Institute of Geophysics and Geoinformatics, TU Bergakademie Freiberg View all articles by this author Metrics & Citations Metrics Article Usage 387 views 273 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Magued Al-Aghbary, Mohamed Osman Awaleh, Mohamed Jalludin, et al. Improving Geothermal Heat Flow Predictions and Uncertainty Quantification using Clustering-based Quantile Regression Forests. Authorea . 28 July 2025. DOI: https://doi.org/10.22541/au.175373261.14525669/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); Cited by Shaoxia Liu, Xueyuan Tang, Shuhu Yang, Lijuan Wang, Jianjie Liu, Mapping Antarctic geothermal heat flow with deep neural networks optimized by particle swarm optimization algorithm, The Cryosphere, 20 , 3, (1543-1558), (2026). https://doi.org/10.5194/tc-20-1543-2026 Crossref Loading... View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.175373261.14525669/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9ffb5bf50d8c1b23',t:'MTc3OTQ0ODA2Nw=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();