Mineral resource estimation using spatial copulas and machine learning optimized with metaheuristics in a copper deposit

Mineral resource estimation using spatial copulas and machine learning optimized with metaheuristics in a copper deposit | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mineral resource estimation using spatial copulas and machine learning optimized with metaheuristics in a copper deposit Marco A. Cotrina-Teatino, Jairo J. Marquina-Araujo, Jose N. Mamani-Quispe, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6823296/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Sep, 2025 Read the published version in Earth Science Informatics → Version 1 posted 12 You are reading this latest preprint version Abstract This study aimed to estimate mineral resources using spatial copula models (Gaussian, t-Student, Frank, Clayton, and Gumbel) and machine learning algorithms, including Random Forest (RF), Support Vector Regression (SVR), XGBoost, Decision Tree (DT), K-Nearest Neighbors (KNN), and Artificial Neural Networks (ANN), optimized through metaheuristics such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Genetic Algorithms (GA) in a copper deposit in Peru. The dataset consisted of 185 diamond drill holes, from which 5,654 15-meter composites were generated. Model validation was performed using leave-one-out cross-validation (LOO) and grade–tonnage curve analysis on a block model containing 381,774 units. Results show that copulas outperformed ordinary kriging (OK) in terms of estimation accuracy and their ability to capture spatial variability. The Frank copula achieved R 2 = 0.78 and MAE = 0.09, while the Clayton copula reached R 2 = 0.72 with a total estimated resource of 2,426.42 Mt of copper, compared to 2,202.57 Mt estimated by OK (R 2 = 0.69, MAE = 0.10). Among the machine learning models, the best performance was achieved by KNN + GA, with R 2 = 0.82, RMSE = 0.12, a mean grade of 0.3278%, and a total resource of 2,302.68 Mt. Other models such as RF + PSO and XGBoost + ACO also delivered strong results, with resources exceeding 2,050 Mt and R 2 values of 0.63. In conclusion, copulas and machine learning are robust alternatives to OK. Rather than being exclusive, they can be combined based on deposit type and project context to improve the reliability and quality of resource estimation. Mineral resource estimation Spatial copulas Machine learning Metaheuristics Geostatistics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 30 Sep, 2025 Read the published version in Earth Science Informatics → Version 1 posted Editorial decision: Revision requested 12 Jul, 2025 Reviews received at journal 02 Jul, 2025 Reviews received at journal 01 Jul, 2025 Reviewers agreed at journal 18 Jun, 2025 Reviewers agreed at journal 18 Jun, 2025 Reviewers agreed at journal 18 Jun, 2025 Reviewers agreed at journal 16 Jun, 2025 Reviewers agreed at journal 15 Jun, 2025 Reviewers invited by journal 15 Jun, 2025 Editor assigned by journal 15 Jun, 2025 Submission checks completed at journal 05 Jun, 2025 First submitted to journal 04 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6823296","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471727554,"identity":"35ebb03a-53fe-4b72-bc0a-929f5192db05","order_by":0,"name":"Marco A. 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The dataset consisted of 185 diamond drill holes, from which 5,654 15-meter composites were generated. Model validation was performed using leave-one-out cross-validation (LOO) and grade\u0026ndash;tonnage curve analysis on a block model containing 381,774 units. Results show that copulas outperformed ordinary kriging (OK) in terms of estimation accuracy and their ability to capture spatial variability. The Frank copula achieved R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.78 and MAE\u0026thinsp;=\u0026thinsp;0.09, while the Clayton copula reached R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.72 with a total estimated resource of 2,426.42 Mt of copper, compared to 2,202.57 Mt estimated by OK (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.69, MAE\u0026thinsp;=\u0026thinsp;0.10). Among the machine learning models, the best performance was achieved by KNN\u0026thinsp;+\u0026thinsp;GA, with R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.82, RMSE\u0026thinsp;=\u0026thinsp;0.12, a mean grade of 0.3278%, and a total resource of 2,302.68 Mt. Other models such as RF\u0026thinsp;+\u0026thinsp;PSO and XGBoost\u0026thinsp;+\u0026thinsp;ACO also delivered strong results, with resources exceeding 2,050 Mt and R\u003csup\u003e2\u003c/sup\u003e values of 0.63. In conclusion, copulas and machine learning are robust alternatives to OK. Rather than being exclusive, they can be combined based on deposit type and project context to improve the reliability and quality of resource estimation.\u003c/p\u003e","manuscriptTitle":"Mineral resource estimation using spatial copulas and machine learning optimized with metaheuristics in a copper deposit","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-17 11:09:17","doi":"10.21203/rs.3.rs-6823296/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-12T20:14:48+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-03T01:56:53+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-01T12:39:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"331338056452556683917953245918107717152","date":"2025-06-18T06:17:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"104310510925182140421752137694388777018","date":"2025-06-18T05:57:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251766124177260917295756377146423506627","date":"2025-06-18T04:36:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"102023589613030765703099474614245800337","date":"2025-06-16T04:35:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"319044754883506988792374215184841715206","date":"2025-06-15T17:49:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-15T17:47:13+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-15T17:45:40+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-06T02:19:17+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth Science Informatics","date":"2025-06-04T19:45:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"earth-science-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"esin","sideBox":"Learn more about [Earth Science Informatics](http://link.springer.com/journal/12145)","snPcode":"12145","submissionUrl":"https://submission.nature.com/new-submission/12145/3","title":"Earth Science Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"cca839db-91f2-4e7b-8a99-d31aec394a53","owner":[],"postedDate":"June 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-06T16:01:11+00:00","versionOfRecord":{"articleIdentity":"rs-6823296","link":"https://doi.org/10.1007/s12145-025-02009-2","journal":{"identity":"earth-science-informatics","isVorOnly":false,"title":"Earth Science Informatics"},"publishedOn":"2025-09-30 15:57:20","publishedOnDateReadable":"September 30th, 2025"},"versionCreatedAt":"2025-06-17 11:09:17","video":"","vorDoi":"10.1007/s12145-025-02009-2","vorDoiUrl":"https://doi.org/10.1007/s12145-025-02009-2","workflowStages":[]},"version":"v1","identity":"rs-6823296","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6823296","identity":"rs-6823296","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}