Graph Neural Operator: A DeepONet-Based Framework for Learning Thermo-Mechanical Distortion in Metallic Additive Manufacturing

Graph Neural Operator: A DeepONet-Based Framework for Learning Thermo-Mechanical Distortion in Metallic Additive Manufacturing | 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 Article Graph Neural Operator: A DeepONet-Based Framework for Learning Thermo-Mechanical Distortion in Metallic Additive Manufacturing haochen mu, Zhonghao chen, Lei Yuan, Zhao Zhang, Hongtao Zhu, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7304515/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 Recent advances in machine learning (ML) have enabled efficient modelling of process-structure-property relationships in metallic additive manufacturing (AM), offering promising alternatives to conventional simulation-based methods. However, most ML models rely on input-output regression paradigms, which limit their ability to generalize to unseen scenarios. This paper proposes a graph neural operator that integrates deep operator network (DeepONet) with graph neural networks (GNNs) to simulate the thermo-mechanical constitutive behaviour in metallic AM. The proposed DeepONet-GNN framework decouples the thermal and structural fields, leveraging sparse temperature measurements to predict full-field z-direction distortion across unseen geometries. Through layer-wise evaluations on multiple structures, the model demonstrates strong generalization, data efficiency, and robustness to variations in sensor distribution, achieving a low RMSE of 0.0881 mm. Compared to a coupled GNN, DeepONet-GNN reaches convergence with similar accuracy using 50% fewer training epochs. The proposed DeepONet-GNN model demonstrates the ability to generalize to unseen geometries while leveraging only 5% of the temperature sensor data, highlighting the potential of graph neural operators as accurate and scalable surrogates for real-time prediction in AM processes. Physical sciences/Engineering/Mechanical engineering Physical sciences/Materials science/Theory and computation/Computational methods Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Mathematics and computing/Computer science Additive Manufacturing machine learning digital twins graph neural networks DeepONet Full Text Additional Declarations There is NO Competing Interest. CRediT author statement Zhonghao Chen : Conceptualization, Methodology, Software, Writing - Original Draft, Writing - Review & Editing Haochen Mu : Conceptualization, Methodology, Software, Writing - Review & Editing Zhao Zhang : Data Curation, Software Lei Yuan : Writing - Review & Editing, Data Curation, Validation Hongtao Zhu : Supervision, Resources, Writing - Review & Editing Ninshu Ma : Supervision, Writing - Review & Editing Zengxi Pan : Conceptualization, Supervision, Writing - Review & Editing 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. 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-7304515","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":500072441,"identity":"ba96ffec-d427-4ee4-9e01-bcc0e5c0033f","order_by":0,"name":"haochen mu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYFACHhBxgIGBvYHBAMhKAGIDIrXwHGAwOECaFokEMEVYi+6M3IMfPtTckTOXfHug+EOFXR4De/M2CYaaOzi1mN3IS5acceyZseXsvASDA2eSixl4jpVJMBx7hkdLjoE0b8PhxA23cwwMDrYdSGyQyDGTYGw4jE+L8W+glvoNN88AtfwDapF/Q1CLGciWBIMbPEAtDSBbeAhoOfPGzHLGscOGG84AHXbmWHJiG09asUXCMTxajucY3/hQc1je4PgZM4OKGrvEfvbDG0EiOLUgAzZwfLCBiASiNDAwMD8gUuEoGAWjYBSMMAAAlURdTh4zwGkAAAAASUVORK5CYII=","orcid":"","institution":"Nanjing Tech University","correspondingAuthor":true,"prefix":"","firstName":"haochen","middleName":"","lastName":"mu","suffix":""},{"id":500072442,"identity":"e0900dab-161b-44b2-808a-82932753ed38","order_by":1,"name":"Zhonghao chen","email":"","orcid":"https://orcid.org/0009-0008-7183-6290","institution":"Nanjing Tech University","correspondingAuthor":false,"prefix":"","firstName":"Zhonghao","middleName":"","lastName":"chen","suffix":""},{"id":500072443,"identity":"e068dd30-9c7b-452c-95b2-9046ada29ecd","order_by":2,"name":"Lei Yuan","email":"","orcid":"","institution":"Nanjing Tech University","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"Yuan","suffix":""},{"id":500072444,"identity":"d6e5c6ca-be85-4d1c-aec0-7950cb46f3f3","order_by":3,"name":"Zhao Zhang","email":"","orcid":"https://orcid.org/0009-0003-9548-4836","institution":"University of Wollongong","correspondingAuthor":false,"prefix":"","firstName":"Zhao","middleName":"","lastName":"Zhang","suffix":""},{"id":500072445,"identity":"e2aa1e90-2abc-4f52-b0b3-6caef5fee35e","order_by":4,"name":"Hongtao Zhu","email":"","orcid":"https://orcid.org/0000-0003-1405-7828","institution":"University of Wollongong, Australia","correspondingAuthor":false,"prefix":"","firstName":"Hongtao","middleName":"","lastName":"Zhu","suffix":""},{"id":500072446,"identity":"bdd09c1e-6346-49f3-862f-542d51b51d34","order_by":5,"name":"Ninshu Ma","email":"","orcid":"","institution":"Japan Welding and Joining Research Institute, Osaka University","correspondingAuthor":false,"prefix":"","firstName":"Ninshu","middleName":"","lastName":"Ma","suffix":""},{"id":500072447,"identity":"21a20957-ef11-4e1c-a5f2-75b4ba8fe886","order_by":6,"name":"Zengxi Pan","email":"","orcid":"","institution":"University of Wollongong","correspondingAuthor":false,"prefix":"","firstName":"Zengxi","middleName":"","lastName":"Pan","suffix":""}],"badges":[],"createdAt":"2025-08-06 01:05:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7304515/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7304515/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91216327,"identity":"4fa17d44-5d8c-4ae6-baaa-c41807eab636","added_by":"auto","created_at":"2025-09-12 19:48:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2958900,"visible":true,"origin":"","legend":"","description":"","filename":"GraphNeuralOperatorwithdetails.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7304515/v1_covered_b3170099-b364-45e6-9673-8e64b59e9929.pdf"}],"financialInterests":"\u003cp\u003eThere is \u003cstrong\u003eNO\u003c/strong\u003e Competing Interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT author statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eZhonghao Chen\u003c/strong\u003e: Conceptualization, Methodology, Software, Writing - Original Draft, Writing - Review \u0026amp; 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