Optimization of 2D Finite Element Meshes using Valence-Aware Neural Smoothing

Optimization of 2D Finite Element Meshes using Valence-Aware Neural Smoothing | 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 Optimization of 2D Finite Element Meshes using Valence-Aware Neural Smoothing Olivier R. Gouveia, José M. Guedes, Rui B. Ruben This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8265287/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract The quality of computational meshes is a critical factor in ensuring the accuracy, stability, and efficiency of numerical simulations, particularly within the framework of finite element analysis (FEA). Classical mesh smoothing techniques, such as Laplacian smoothing and optimization-based methods, are commonly employed to enhance element shape and distribution. However, these approaches are constrained either by the inability to explicitly account for mesh quality metrics, in the case of Laplacian smoothing, or by high computational cost, in the case of optimization-based methods.Recent advances in machine learning, and neural networks in particular, provide a promising alternative to address these limitations. Yet, existing approaches typically require separate models for each mesh topology or rely on computationally intensive architectures, limiting their scalability in practice.To overcome these challenges, we propose a Valence-Aware Smoothing Optimization Network (VASONet), a dual-branch neural architecture capable of handling multiple mesh configurations within a single model. By explicitly encoding the valence degree of local nodal neighborhoods into the learning process, VASONet achieves both flexibility across topologies and efficiency in computation, eliminating the need for multiple specialized models.Numerical experiments demonstrate that VASONet provides a fast and robust alternative to conventional optimization-based methods, generating high-quality meshes with improved geometric and numerical properties while reducing the computational time by 34 \((\times)\) , in average. These results highlight the potential of VASONet as a scalable and generalizable framework for mesh smoothing and optimization in computational mechanics. Mesh Smoothing Mesh Optimization Neural Network Valence Embedding Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 18 Feb, 2026 Reviews received at journal 18 Feb, 2026 Reviewers agreed at journal 22 Jan, 2026 Reviewers invited by journal 21 Jan, 2026 Editor assigned by journal 02 Dec, 2025 Submission checks completed at journal 02 Dec, 2025 First submitted to journal 26 Nov, 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-8265287","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":578587335,"identity":"f278633e-bd87-4adc-a952-fb10cd9762c6","order_by":0,"name":"Olivier R. 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Smoothing","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Mesh Smoothing, Mesh Optimization, Neural Network, Valence Embedding","lastPublishedDoi":"10.21203/rs.3.rs-8265287/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8265287/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe quality of computational meshes is a critical factor in ensuring the accuracy, stability, and efficiency of numerical simulations, particularly within the framework of finite element analysis (FEA). Classical mesh smoothing techniques, such as Laplacian smoothing and optimization-based methods, are commonly employed to enhance element shape and distribution. However, these approaches are constrained either by the inability to explicitly account for mesh quality metrics, in the case of Laplacian smoothing, or by high computational cost, in the case of optimization-based methods.Recent advances in machine learning, and neural networks in particular, provide a promising alternative to address these limitations. Yet, existing approaches typically require separate models for each mesh topology or rely on computationally intensive architectures, limiting their scalability in practice.To overcome these challenges, we propose a Valence-Aware Smoothing Optimization Network (VASONet), a dual-branch neural architecture capable of handling multiple mesh configurations within a single model. By explicitly encoding the valence degree of local nodal neighborhoods into the learning process, VASONet achieves both flexibility across topologies and efficiency in computation, eliminating the need for multiple specialized models.Numerical experiments demonstrate that VASONet provides a fast and robust alternative to conventional optimization-based methods, generating high-quality meshes with improved geometric and numerical properties while reducing the computational time by 34\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\times)\\)\u003c/span\u003e\u003c/span\u003e, in average. These results highlight the potential of VASONet as a scalable and generalizable framework for mesh smoothing and optimization in computational mechanics.\u003c/p\u003e","manuscriptTitle":"Optimization of 2D Finite Element Meshes using Valence-Aware Neural Smoothing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-23 04:19:30","doi":"10.21203/rs.3.rs-8265287/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-18T16:06:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-18T14:29:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"197703328441420145293195852157630224572","date":"2026-01-22T07:55:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-21T17:41:59+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-03T03:55:14+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-03T03:51:03+00:00","index":"","fulltext":""},{"type":"submitted","content":"Engineering with Computers","date":"2025-11-26T11:07:10+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8835bdf8-c7b6-4bf6-b0c0-017e9503805d","owner":[],"postedDate":"January 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-04T13:39:02+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-23 04:19:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8265287","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8265287","identity":"rs-8265287","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}