Comparative Modeling of Nuclear Energy Consumption in the United States and France: An Optimized Structure-Adaptive Grey Model

Comparative Modeling of Nuclear Energy Consumption in the United States and France: An Optimized Structure-Adaptive Grey Model | 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 Comparative Modeling of Nuclear Energy Consumption in the United States and France: An Optimized Structure-Adaptive Grey Model Alae Chahid, Naima Shifa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7250236/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study investigates nuclear energy consumption trends in the United States, and France by applying advanced time-series modeling and computational optimization techniques. Using annual consumption data from 2005 to 2023, the research compares the predictive accuracy under data scarcity of the AutoRegressive Integrated Moving Average (ARIMA), Grey Model (1,1,t), Grey Model(1,1,t²), and an Optimized Structure-Adaptive Grey Model (OSGM). This OSGM (1,1,t \(\:{}^{\lambda\:})\:\) extends the traditional Grey Model (1,1) by introducing time-dependent terms and parameter tuning through particle swarm optimization and Monte Carlo simulations. Models are trained and tested using an in-sample and out-of-sample period framework. Then, forecast accuracies are compared using Mean Absolute Percentage Error, and the Root Mean Squared Error. The results show that the new Optimized Structured Grey Model and the ARIMA models surpass the other models in achieving accuracy forecasts. While ARIMA performs well with sufficient data, the OSGM model, however, offers greater adaptability to nonlinear patterns and structural shifts, adapting to country-specific dynamics. The integration of informatics-driven optimization into grey system modeling presents a viable approach for energy forecasting in data-constrained environments. These results validate the model's suitability for situations with limited data and offer a useful tool for climate-aligned decision-making and sustainable energy planning. Nuclear energy grey model Energy Consumption Modeling Optimized Structure-Adaptive Model forecasting ARIMA Monte Carlo simulation Particle Swarm Optimization Energy Informatics Data-driven Modeling Time-series Analysis Mean-Absolute Percentage Root Mean Squared Error USA France Energy dynamics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-7250236","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":502509512,"identity":"38690a4f-d51b-4052-947c-3067ebde6340","order_by":0,"name":"Alae Chahid","email":"data:image/png;base64,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","orcid":"","institution":"DePauw University","correspondingAuthor":true,"prefix":"","firstName":"Alae","middleName":"","lastName":"Chahid","suffix":""},{"id":502509513,"identity":"769fe3fe-9d37-409f-b6c7-1653c77823df","order_by":1,"name":"Naima Shifa","email":"","orcid":"","institution":"DePauw University","correspondingAuthor":false,"prefix":"","firstName":"Naima","middleName":"","lastName":"Shifa","suffix":""}],"badges":[],"createdAt":"2025-07-30 08:08:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7250236/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7250236/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98437269,"identity":"eb998230-2d26-4b6b-b0cc-2f82241fe711","added_by":"auto","created_at":"2025-12-17 16:57:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":606105,"visible":true,"origin":"","legend":"","description":"","filename":"EnergyInformaticsJournal1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7250236/v1_covered_da4cc69d-9a9d-4487-9e5c-f8d155a23e96.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":" Comparative Modeling of Nuclear Energy Consumption in the United States and France: An Optimized Structure-Adaptive Grey Model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Nuclear energy, grey model, Energy Consumption Modeling, Optimized Structure-Adaptive Model forecasting, ARIMA, Monte Carlo simulation, Particle Swarm Optimization, Energy Informatics, Data-driven Modeling, Time-series Analysis, Mean-Absolute Percentage, Root Mean Squared Error, USA, France, Energy dynamics","lastPublishedDoi":"10.21203/rs.3.rs-7250236/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7250236/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates nuclear energy consumption trends in the United States, and France by applying advanced time-series modeling and computational optimization techniques. 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