Towards Unified Material-State Tensors for Physics-Gated AI Thermodynamic Admissibility as Constitutional Constraint

Towards Unified Material-State Tensors for Physics-Gated AI Thermodynamic Admissibility as Constitutional Constraint | 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 Towards Unified Material-State Tensors for Physics-Gated AI Thermodynamic Admissibility as Constitutional Constraint Santhosh Shyamsundar, Santosh Prabhu Shenbagamoorthy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8900728/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract AI systems for physical design lack formal safety guarantees. We ground safety in thermodynamics using a predictor-agnostic hard gate that rejects violating predictions from any ML model, extending constitutional AI to continuous domains. We introduce the Unified Material-State Tensor (UMST) , validated by physics engines enforcing the Clausius-Duhem inequality. Unlike soft-constraint baselines, we prove accepted predictions satisfy the second law of thermodynamics within the constitutive model's validity (Theorem 1). While demonstrated with a fixed 64-dimensional vector, UMST scales to ℝ^(H×W×D×F) sparse tensors, enabling multi-scale physics ML . Our DUMSTO framework achieves 100% admissibility (vs. 88–100% baselines) with competitive accuracy and faster inference, ensuring all predictions are thermodynamically admissible for safely replanning generative design. Artificial Intelligence and Machine Learning Artificial Intelligence AI Safety Thermodynamics Materials Science Physics-Constrained Machine Learning Constitutive Modelling Real-time Systems Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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-8900728","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":597083688,"identity":"7d736fcc-78de-43f6-aebd-a8261130bf92","order_by":0,"name":"Santhosh Shyamsundar","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0000-4552-6477","institution":"IAAC","correspondingAuthor":true,"prefix":"","firstName":"Santhosh","middleName":"","lastName":"Shyamsundar","suffix":""},{"id":597083689,"identity":"d8d44413-ef20-4e7e-8817-c1efa895bf40","order_by":1,"name":"Santosh Prabhu Shenbagamoorthy","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0005-5089-7498","institution":"IAAC","correspondingAuthor":true,"prefix":"","firstName":"Santosh","middleName":"Prabhu","lastName":"Shenbagamoorthy","suffix":""}],"badges":[],"createdAt":"2026-02-17 11:49:56","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8900728/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-8900728/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104397636,"identity":"02c9ec4c-0a68-4105-9074-304478c74ebd","added_by":"auto","created_at":"2026-03-11 11:53:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1258249,"visible":true,"origin":"","legend":"","description":"","filename":"TowardsUMSTv3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8900728/v2_covered_e252aacf-2896-4c0e-b49b-51aef489dcea.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Towards Unified Material-State Tensors for Physics-Gated AI\nThermodynamic Admissibility as Constitutional Constraint","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"IAAC","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":"Artificial Intelligence,AI Safety,Thermodynamics,Materials Science,Physics-Constrained Machine Learning,Constitutive Modelling, Real-time Systems","lastPublishedDoi":"10.21203/rs.3.rs-8900728/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8900728/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAI systems for physical design lack formal safety guarantees. We ground safety in thermodynamics using a\u0026nbsp;\u003cstrong\u003epredictor-agnostic hard gate\u003c/strong\u003e\u0026nbsp;that rejects violating predictions from any ML model, extending constitutional AI to continuous domains. We introduce the\u0026nbsp;\u003cstrong\u003eUnified Material-State Tensor (UMST)\u003c/strong\u003e, validated by physics engines enforcing the Clausius-Duhem inequality. Unlike soft-constraint baselines, we prove accepted predictions satisfy the second law of thermodynamics within the constitutive model's validity (Theorem 1). While demonstrated with a fixed 64-dimensional vector, UMST scales to ℝ^(H×W×D×F) sparse tensors, enabling\u0026nbsp;\u003cstrong\u003emulti-scale physics ML\u003c/strong\u003e. 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