Flexible Clustering of Substations for Accurate and Rapid Hybrid Simulation of District Heating

Flexible Clustering of Substations for Accurate and Rapid Hybrid Simulation of District Heating | 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 Flexible Clustering of Substations for Accurate and Rapid Hybrid Simulation of District Heating Dubon Rodrigue, Mohamed Tahar Mabrouk, Bastien Pasdeloup, Patrick Meyer, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8658784/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract District Heating Networks (DHNs) are crucial to decarbonizing the heat supply sector, with the evolution toward 4th and 5th generation systems offering significant potential for efficiency. However, the increasing complexity of these modern systems makes high-fidelity dynamic thermo-hydraulic simulation computationally intensive, particularly for large-scale networks. Recent research has utilized Machine Learning (ML)-based surrogate models to replace substation clusters, reducing spatial complexity and accelerating simulations. Yet, the efficacy of this spatial reduction is highly sensitive to the clusters definition. Poorly selected clusters degrade the surrogate models accuracy and undermine the simulation performance. This paper proposes a flexible, task-driven graph clustering methodology specifically designed for ML-based spatial reduction. We introduce physics-informed distance metrics that encode the primary drivers of ML surrogate model errors. These distance metrics are leveraged within a hierarchical agglomerative clustering framework. The methodology is evaluated across 16 DHNs with diverse topological and thermal characteristics. Our results reveal a clear, generalizable trade-off between simulation accuracy and computational time reduction, allowing the integration of user-preferences. On an independent validation DHN, a high physical accuracy preference yielded a deviation 6.45 MWh of the total thermal energy produced estimation (3.76% of total thermal losses within the network), albeit with modest computational gains. Conversely, a high spatial reduction preference achieved a 91% decrease in computational time, at the cost of a 45.24 MWh error, representing 26.37% error relative to thermal losses. These findings demonstrate that the proposed clustering framework provides a robust and flexible tool to calibrate the balance between physical fidelity of the simulation and computational speed across varying DHN generations. District Heating Clustering Surrogate Models Machine Learning Hybrid Simulation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 21 Mar, 2026 Reviews received at journal 11 Mar, 2026 Reviewers agreed at journal 09 Mar, 2026 Reviewers agreed at journal 05 Mar, 2026 Reviewers agreed at journal 05 Mar, 2026 Reviewers agreed at journal 10 Feb, 2026 Reviewers invited by journal 05 Feb, 2026 Editor assigned by journal 23 Jan, 2026 Submission checks completed at journal 23 Jan, 2026 First submitted to journal 21 Jan, 2026 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. 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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-8658784","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":579119391,"identity":"1a3d1137-ed85-4fee-a0c3-5bc33775077c","order_by":0,"name":"Dubon 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Heating","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"energy-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"einf","sideBox":"Learn more about [Energy Informatics](https://energyinformatics.springeropen.com)","snPcode":"42162","submissionUrl":"https://submission.nature.com/new-submission/42162/3","title":"Energy Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"District Heating, Clustering, Surrogate Models, Machine Learning, Hybrid Simulation","lastPublishedDoi":"10.21203/rs.3.rs-8658784/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8658784/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDistrict Heating Networks (DHNs) are crucial to decarbonizing the heat supply sector, with the evolution toward 4th and 5th generation systems offering significant potential for efficiency. However, the increasing complexity of these modern systems makes high-fidelity dynamic thermo-hydraulic simulation computationally intensive, particularly for large-scale networks. Recent research has utilized Machine Learning (ML)-based surrogate models to replace substation clusters, reducing spatial complexity and accelerating simulations. Yet, the efficacy of this spatial reduction is highly sensitive to the clusters definition. Poorly selected clusters degrade the surrogate models accuracy and undermine the simulation performance. This paper proposes a flexible, task-driven graph clustering methodology specifically designed for ML-based spatial reduction. We introduce physics-informed distance metrics that encode the primary drivers of ML surrogate model errors. These distance metrics are leveraged within a hierarchical agglomerative clustering framework. The methodology is evaluated across 16 DHNs with diverse topological and thermal characteristics. Our results reveal a clear, generalizable trade-off between simulation accuracy and computational time reduction, allowing the integration of user-preferences. On an independent validation DHN, a high physical accuracy preference yielded a deviation 6.45 MWh of the total thermal energy produced estimation (3.76% of total thermal losses within the network), albeit with modest computational gains. Conversely, a high spatial reduction preference achieved a 91% decrease in computational time, at the cost of a 45.24 MWh error, representing 26.37% error relative to thermal losses. These findings demonstrate that the proposed clustering framework provides a robust and flexible tool to calibrate the balance between physical fidelity of the simulation and computational speed across varying DHN generations.\u003c/p\u003e","manuscriptTitle":"Flexible Clustering of Substations for Accurate and Rapid Hybrid Simulation of District Heating","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-27 03:31:26","doi":"10.21203/rs.3.rs-8658784/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-21T12:27:01+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-11T10:23:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"18239638308564533626165111905742285205","date":"2026-03-09T23:08:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"313015270396363996156492941557251023344","date":"2026-03-05T16:58:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"4209418004975456123442639620563897120","date":"2026-03-05T09:49:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87339780716213798914426753512568301288","date":"2026-02-10T21:09:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-05T17:49:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-23T05:38:46+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-23T05:37:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Energy Informatics","date":"2026-01-21T10:41:26+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"energy-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"einf","sideBox":"Learn more about [Energy Informatics](https://energyinformatics.springeropen.com)","snPcode":"42162","submissionUrl":"https://submission.nature.com/new-submission/42162/3","title":"Energy Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1e34bf87-969f-4c49-8936-c3b64d952fe9","owner":[],"postedDate":"January 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-02T11:40:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-27 03:31:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8658784","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8658784","identity":"rs-8658784","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}