[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119672-en":3,"doc-seo-119672-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119672,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","A peridynamic-based machine learning model for one-dimensional and two-dimensional structures - Research overview","The work addresses limitations of purely data-driven prediction for complex physical phenomena where data scarcity reduces robustness. It introduces a peridynamics-based machine learning framework that combines physics-consistent peridynamic modeling with a theory-guided learning component. Linear regression is used to obtain relationships linking material point displacement to related family member displacements and applied forces, and a numerical coupling procedure is provided. The coupled model’s accuracy is verified on representative one-dimensional bars and two-dimensional plates, then extended to damage prediction for cracked plates and dynamic loading simulations.","Continuum Mech. Thermodyn.  \n[https://doi.org/10.1007/s00161-020-00905-0](https://doi.org/10.1007/s00161-020-00905-0)  \nORIGINAL ARTICLE  \nCong Tien Nguyen · Selda Oterkus · Erkan Oterkus  \nA peridynamic-based machine learning model for one-dimensional and two-dimensional structures  \nReceived: 27 January 2020 / Accepted: 23 July 2020 © The Author(s) 2020  \nAbstract With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics-based machine learning model for one-and twodimensional structures. The linear relationships between the displacement of a material point and displacementsofits family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction fora plate with a preexisting crack, a two-dimensional representation of a three-point bending test and a plate subjected to dynamic load are simulated.  \nKeywords Machine learning · Peridynamics · Fracture · Peridynamic-based machine learning · Linear regression  \n1 Introduction  \nPredicting progressive failures in structures is a challenging task in engineering. The classical continuum mechanics faces conceptual and mathematical difficulties in terms of predicting crack nucleation and growth, especially for multiple crack paths because it uses differential equations. In contrast, peridynamics (PD) is anonlocal theory representing material behavior by using integro-differential equations that are valid in both continuous and discontinuous models [1–5] . Therefore, PD is suitable for predicting progressive damages.  \nPeridynamics can be applicable for both elastic and plastic materials [6–10], composite and polycrystalline materials [11–16], multiphysics [17–19], large deformation problems [20], topology optimization [21] and multiscale modeling [22, 23] . Peridynamics can also be suitable for structural idealization to analyze slender structures by using PD beam models [24–27] or thin wall structures by using PD plate and shell models [27– 32] . Moreover, peridynamic differential operator is used to approximate field variables and their temporal and spatial derivatives for the conversion of the local form of differentiation to its nonlocal integral form [33–36] .  \nCommunicated by Luca Placidi.  \nC. Tien · S. Oterkus (B) · E. Oterkus  \nDepartment of Naval Architecture, Ocean and Marine Engineering, PeriDynamics Research Centre (PDRC), University of Strathclyde, Glasgow, UK  \nE-mail: [selda.oterkus@strath.ac.uk](selda.oterkus@strath.ac.uk)  \nPeridynamics can also be combined with other well-known numerical methods such as finite element analysis (FEA) [12, 37–39] or smooth particle method [40, 41], or computational fluid dynamics (CFD) [42] . Extensive literature surveys on peridynamics are given in [4, 5, 43] .  \nHowever, similar to other physics-based models, solving PD equations ofmotion could be time-consuming, especially when real-time predictions on live data are required. In contrast, with the support of computer resources as well as the rapid growth of available data, artificial intelligence (AI), machine learning (ML) and data analytics are providing an alternative solution for physics-based models. These data-driven m","cbCaioA6fgmewQrB","https://ap.wps.com/l/cbCaioA6fgmewQrB","pdf",8858954,1,33,"English","en",105,"# Abstract\n# 1 Introduction\n## Progressive failure prediction challenges\n## Why peridynamics for discontinuities\n## Applications and numerical background\n## Coupling machine learning with physics models\n## Related work on neural networks and fracture prediction\n# Keywords","[{\"question\":\"Why does the study propose theory-guided data science instead of purely data-driven models?\",\"answer\":\"Purely data-driven approaches can lack robustness when physical phenomena have limited data, leading to weaker predictive performance. Theory-guided data science leverages both physics-driven structure and learning from data.\"},{\"question\":\"How is the machine learning model constructed in the proposed framework?\",\"answer\":\"The model uses linear regression to derive linear relationships between a material point’s displacement and the displacements of its family members, together with the applied forces.\"},{\"question\":\"How is the coupled peridynamic–machine learning model validated?\",\"answer\":\"Accuracy is verified using examples including a one-dimensional bar and two-dimensional plate cases, followed by simulations for damage prediction with a preexisting crack and dynamic loading problems.\"}]","A peridynamic-based machine learning model for one-dimensional and two-dimensional structures - Research overview | PDF",1785725625,83,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"a-peridynamic-based-machine-learning-model-for-one-dimensional-and-two-dimensional-structures-research-overview","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/a-peridynamic-based-machine-learning-model-for-one-dimensional-and-two-dimensional-structures-research-overview/119672/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does the study propose theory-guided data science instead of purely data-driven models?","Question",{"text":75,"@type":76},"Purely data-driven approaches can lack robustness when physical phenomena have limited data, leading to weaker predictive performance. Theory-guided data science leverages both physics-driven structure and learning from data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the machine learning model constructed in the proposed framework?",{"text":80,"@type":76},"The model uses linear regression to derive linear relationships between a material point’s displacement and the displacements of its family members, together with the applied forces.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the coupled peridynamic–machine learning model validated?",{"text":84,"@type":76},"Accuracy is verified using examples including a one-dimensional bar and two-dimensional plate cases, followed by simulations for damage prediction with a preexisting crack and dynamic loading problems.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]