[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118958-en":3,"doc-seo-118958-105":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},118958,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Enhancement of a structural optimization simulation tool using Machine Learning","The thesis addresses topology optimization for linear elastic structures by integrating machine learning to reduce computational cost. It exploits additive manufacturing-inspired synergies with topology optimization, using anisotropic mesh adaptation to obtain strongly defined configurations and support structures under external loads. The project investigates graph neural networks to generate quasi-optimal meshes as an initialization for existing pipelines. The method relies on reproducing anisotropic finite-element elements and validating the approach through numerical reconstruction and performance results.","Double Master’s Degree Program  \nUniversità degli Studi di Padova Dipartimento di Ingegneria Civile, Edile ed Ambientale  \nMathematical Engineering  \nMathematical Modelling for Engineering and Science  \nUniversitat Politècnica de Catalunya Departament d’Enginyeria Civil i Ambiental  \nNumerical Methods in Engineering  \nFinal Master’s Thesis  \nEnhancement of a structural optimization simulation tool using Machine Learning  \nCandidate: Zamberlan Giorgio  \nUniPd Supervisor: Larese Antonia  \nUniPd Co-supervisor: Putti Mario  \nUPC Supervisor: Giacomini Matteo  \nAcademic year 2022/2023  \nAbstract  \nAdditive manufacturing has opened unexplored possibilities in the fabrication of elastic structures not manufacturable via traditional moulding and machining processes. These new fabrication techniques found immediate synergies with topology optimization problems, allowing for the printing process of optimal shapes. Topology Optimization routines uses a wide variety of methodologies to obtain strongly defined configurations, and the one taken into consideration in this work used an anisotropic mesh adaptation technique to do so.  \nThe focus will be centered around the results of a Topology Optimization routine in the context of a linear elastic problem to determine support structures under external loads.  \nThe goal of this project is to show that Machine Learning algorithms could make a substantial contribution to reducing the computational cost of topological optimisation procedures, by generating quasi-optimal meshes asa starting point for the already existing pipelines. Said triangulations will need to reproduce the anisotropic elements to successfully reduce the computational burden of the the considered optimization procedure.  \nThis work will make use of Graph Neural Networks instead of more traditional ones, aiming to show the inherent correlation between Finite Elements Methods and Graph Theory, possibly enticing further research in potential synergies between the two fields.  \nContents  \n1 Introduction 4  \n2 Topology optimization of a linear elastic structure 6  \n2.1 The elastic Problem ........................................... 6  \n2.2 Minimization of the compliace under a volume constrain ....................... 7  \n2.3 The optimization strategy ........................................ 8  \n2.4 Post processing .............................................. 9  \n2.5 Anisotropic mesh adaptation ...................................... 10  \n2.5.1 Metric of a FEM mesh ...................................... 11  \n2.5.2 Mesh adaptation ......................................... 12  \n3 The Graph Neural Network for quasi-optimal meshes 14  \n3.1 The idea .................................................. 14  \n3.1.1 From metric to graph ...................................... 15  \n3.2 Structure of the GNN .......................................... 16  \n3.2.1 Encoding block .......................................... 16  \n3.2.2 Decoding block .......................................... 16  \n3.2.3 Technical details of the operations ............................... 17  \n3.2.4 Overall GNN architecture .................................... 18  \n3.3 Metric transformations and normalization ............................... 19  \n3.3.1 Transformation applied to the metric .............................. 19  \n3.3.2 Normalization applied to the metric .............................. 20  \n3.3.3 Inverse transformation ...................................... 20  \n4 Numerical validation of the GNN 22  \n4.1 Problem statement and Finite Elements approximation ........................ 22  \n4.2 Mesh reconstruction from the metric .................................. 24  \n4.3 GNN configurations ........................................... 26  \n4.3.1 Monolithic approach ....................................... 26  \n4.3.2 Multi Network approach ..................................... 26  \n4.3.3 Technical details of the architecture .............................. 26  \n4.4 Numeri","cbCailphMIxxZ4gT","https://ap.wps.com/l/cbCailphMIxxZ4gT","pdf",9579245,1,54,"English","en",105,"# Introduction\n# Topology optimization of a linear elastic structure\n## The elastic problem\n## Minimization of compliance under a volume constraint\n## The optimization strategy\n## Post processing\n## Anisotropic mesh adaptation\n### Metric of a FEM mesh\n### Mesh adaptation\n# The Graph Neural Network for quasi-optimal meshes\n## The idea\n### From metric to graph\n## Structure of the GNN\n### Encoding block\n### Decoding block\n### Technical details of the operations\n### Overall GNN architecture\n## Metric transformations and normalization\n### Transformation applied to the metric\n### Normalization applied to the metric\n### Inverse transformation\n# Numerical validation of the GNN\n## Problem statement and Finite Elements approximation\n## Mesh reconstruction from the metric\n## GNN configurations\n### Monolithic approach\n### Multi Network approach\n### Technical details of the architecture\n## Numerical results of the validation\n### The database\n### Monolithic approach results\n### Multi Network approach results\n# Numerical Results for GNN-enhanced Topology Optimization\n## Mesh reconstruction from the metric\n## The database\n## Results\n### One encoding block\n### Three encoding blocks\n### Computational speed up\n## Generalization over different problems\n# Conclusions\n## Further developments","[{\"question\":\"What problem does the thesis focus on in topology optimization?\",\"answer\":\"It focuses on determining support structures for a linear elastic problem under external loads, using topology optimization with anisotropic mesh adaptation to obtain well-defined configurations.\"},{\"question\":\"How does machine learning contribute to computational efficiency?\",\"answer\":\"Machine learning, specifically graph neural networks, generates quasi-optimal meshes that serve as a starting point for existing topology optimization pipelines, aiming to reduce computational cost.\"},{\"question\":\"Why are anisotropic elements important in the proposed pipeline?\",\"answer\":\"The generated triangulations must reproduce anisotropic elements so that they can successfully reduce the computational burden of the considered optimization procedure.\"}]","Enhancement of a structural optimization simulation tool using Machine Learning | PDF",1785721202,136,{"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},"enhancement-of-a-structural-optimization-simulation-tool-using-machine-learning","",{"@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/enhancement-of-a-structural-optimization-simulation-tool-using-machine-learning/118958/",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},"What problem does the thesis focus on in topology optimization?","Question",{"text":75,"@type":76},"It focuses on determining support structures for a linear elastic problem under external loads, using topology optimization with anisotropic mesh adaptation to obtain well-defined configurations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does machine learning contribute to computational efficiency?",{"text":80,"@type":76},"Machine learning, specifically graph neural networks, generates quasi-optimal meshes that serve as a starting point for existing topology optimization pipelines, aiming to reduce computational cost.",{"name":82,"@type":73,"acceptedAnswer":83},"Why are anisotropic elements important in the proposed pipeline?",{"text":84,"@type":76},"The generated triangulations must reproduce anisotropic elements so that they can successfully reduce the computational burden of the considered optimization procedure.","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"]