[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117626-en":3,"doc-seo-117626-105":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},117626,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","SINGLE-SNAPSHOT MACHINE LEARNING FOR SUPER-RESOLUTION OF TURBULENCE - A PREPRINT","Modern machine-learning approaches are often treated as data-hungry, yet turbulence may contradict this assumption because each snapshot can contain richer information than a single generic data file. This study examines whether nonlinear learning can extract physical insights from only one turbulent flow snapshot. It develops a machine-learning super-resolution framework reconstructing high-resolution turbulent fields from low-resolution inputs for two-dimensional decaying turbulence and three-dimensional turbulent channel flow. Results show accurate recovery of vortical structures across Reynolds numbers and demonstrate that even inhomogeneous channel-flow insights can be learned from a single snapshot when physics-guided model design and data collection are used.","arXiv :2409 .04923v2 [physics .flu-dyn] 23 Nov 2024  \nSINGLE-SNAPSHOT MACHINE LEARNING  \nFOR SUPER-RESOLUTION OF TURBULENCE  \nA PREPRINT  \nKai Fukami∗ and Kunihiko Taira  \nDepartment of Mechanical and Aerospace Engineering  \nUniversity of California, Los Angeles, CA 90095, USA  \n∗ Corresponding author: [kfukami1@g.ucla.edu](kfukami1@g.ucla.edu)  \nNovember 26, 2024  \nABSTRACT  \nModern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This study asks the question of whether nonlinear machinelearning techniques can effectively extract physical insights even from as little as a single snapshot of turbulent flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two examples of two-dimensional isotropic turbulence and three-dimensional turbulent channel flow. First, we reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers for two-dimensional decaying turbulence. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We also show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. Second, we perform the single-snapshot super-resolution analysis for turbulent channel flow, showing that it is possible to extract physical insights from a single flow snapshot even with inhomogeneity. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.  \n1 Introduction  \nBy gazing at a turbulent flow acquired from numerical simulation or experiment, we can admire the rich physics that involves swirling, stretching, and diffusion. Turbulence also presents multi-scale characteristics over broad length scales [1] . In high Reynolds number turbulent flows, the rich phenomena and characteristics are exhibited at any instance in time. We argue that even a single snapshot of turbulent flow can hold sufficient information to train machine-learning models. This paper poses a question of whether a commonly used big data set is required for training machine-learning models in studying turbulence.  \nThere have been increased usages of modern machine-learning techniques to analyze, model, estimate, and control turbulent flows [2] . These applications include subgrid-scale modeling [3], reduced-order modeling [4], super resolution/flow reconstruction [5, 6, 7], and flow control [8, 9] . These machine-learning models require enormous amount of training data, which is generally significantly larger than those necessitated by traditional analysis techniques.  \nHowever, it may be possible to extract important flow features without such large data sets since even a single turbulent flow snapshot contains multi-scale, scale-invariant structures. To achieve meaningful learning from a single snapshot, we consider training machine-learning models through subsampling and leveraging turbulent statistics. We further note that it is important that machine-learning models have appropriate architectures and learning formulation that fold in physics [10, 11, 12, 13] .  \nA PREPRINT-NOVEMBER 26, 2024  \nLow resolution flow field data  \nMS model  \nHigh resolution flow field data  \n…  \nFigure 1: Interconnected DSC/MS model [13] for super-resolution reconstruction of turbulent flows.  \nThis study considers data-driven analysis using only a single training snapshot of tur","cbCaibn1PsqsNK2l","https://ap.wps.com/l/cbCaibn1PsqsNK2l","pdf",5609738,1,14,"English","en",105,"# Introduction\n## Machine learning for turbulence and data demands\n## Learning from single snapshots via scale invariance\n# Approach\n## Super-resolution formulation and model training strategy\n## Physics constraints: invariance and multi-scale modeling","[{\"question\":\"Can super-resolution of turbulent flow be learned from only one snapshot?\",\"answer\":\"Yes. The approach trains on subdomains sampled from a single snapshot and can reconstruct high-resolution turbulent fields for independent test snapshots.\"},{\"question\":\"What flow cases are used to validate the single-snapshot method?\",\"answer\":\"Two-dimensional isotropic decaying turbulence and three-dimensional turbulent channel flow are used as examples for the super-resolution analysis.\"},{\"question\":\"How does the method ensure physical consistency when training with limited data?\",\"answer\":\"It uses a carefully designed hybrid multi-scale model and leverages physics-guided data collection based on rotation and shear tensor characteristics, along with invariance requirements.\"}]","SINGLE-SNAPSHOT MACHINE LEARNING FOR SUPER-RESOLUTION OF TURBULENCE - A PREPRINT | PDF",1785677387,35,{"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},"single-snapshot-machine-learning-for-super-resolution-of-turbulence-a-preprint","",{"@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/single-snapshot-machine-learning-for-super-resolution-of-turbulence-a-preprint/117626/",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","2026-08-02",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},"Can super-resolution of turbulent flow be learned from only one snapshot?","Question",{"text":75,"@type":76},"Yes. The approach trains on subdomains sampled from a single snapshot and can reconstruct high-resolution turbulent fields for independent test snapshots.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What flow cases are used to validate the single-snapshot method?",{"text":80,"@type":76},"Two-dimensional isotropic decaying turbulence and three-dimensional turbulent channel flow are used as examples for the super-resolution analysis.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the method ensure physical consistency when training with limited data?",{"text":84,"@type":76},"It uses a carefully designed hybrid multi-scale model and leverages physics-guided data collection based on rotation and shear tensor characteristics, along with invariance requirements.","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"]