[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122607-en":3,"doc-seo-122607-105":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},122607,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Probabilistic Machine Learning to Improve Generalisation of Data-Driven Turbulence Modelling - A Preprint","A probabilistic machine learning model is introduced to augment the k-ω SST turbulence model, aiming to improve separated-flow prediction and the generalisability of learned corrections. The work addresses two key issues in ML-assisted turbulence modelling: reliable transfer to unseen geometries and flow conditions, and efficient use of heterogeneous datasets mixing experiments and simulations. Field inversion combined with an ensemble of Gaussian Process Emulators enables the correction function to adapt while controlling uncertainty. Benchmarks show improved performance for adverse pressure gradient cases and safe reversion to the uncorrected model outside training physics.","arXiv :2301 .09443v1 [ cs .CE] 23 Jan 2023  \nPROBABILISTIC MACHINE LEARNING TO IMPROVE GENERALISATION OF DATA-DRIVEN TURBULENCE  \nMODELLING  \nA PREPRINT  \nJoel Ho  \nIndependent Researcher Oxford, UK  \n[joel.ho@hotmail.com](joel.ho@hotmail.com)  \nNick Pepper  \nThe Alan Turing Institute The British Library London, UK  \n[npepper@turing.ac.uk](npepper@turing.ac.uk)  \nTim Dodwell  \nDepartment of Computer Science University of Exeter Exeter, UK  \nJanuary 24, 2023  \nKeywords Computational Fluid Dynamics; Probabilistic Machine Learning; Field Inversion; Turbulence Modelling; Gaussian Process Emulators; Deep Ensembles  \nABSTRACT  \nA probabilistic machine learning model is introduced to augment the k 􀀀 ! SST turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections.  \nIncreasingly, machine learning methods have been used to leverage experimental and high-fidelity data, improving the accuracy of the Reynolds Averaged Navier Stokes (RANS) turbulence models widely used in industry. A significant challenge for such methods is their ability to generalise to unseen geometries and flow conditions. Furthermore, heterogeneous datasets containing a mix of experimental and simulation data must be efficiently handled. In this work, field inversion and an ensemble of Gaussian Process Emulators (GPEs) is employed to address both of these challenges.  \nThe ensemble model is applied to a range of benchmark test cases, demonstrating improved turbulence modelling for cases with separated flows with adverse pressure gradients, where RANS simulations are understood to be unreliable. Perhaps more significantly, the simulation reverted to the uncorrected model in regions of the flow exhibiting physics outside of the training data.  \n1 Introduction  \nComputational Fluid Dynamics (CFD) allows new aeromechanical designs to be evaluated by modelling the flow around the proposed geometry from first principles. In contrast to simpler correlation based design methods, this has allowed designers to explore the design space beyond the existing design envelope (1) . While this has presented opportunities, the Reynolds-averaged Navier–Stokes (RANS) models, which are typically employed by industry, suffer from fundamental weaknesses that undermine their efficacy as a design tool (2) . Within RANS, the intermediate and small energy scales are modelled rather than resolved directly. This has the effect of making the model inexpensive compared to Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS), where comparatively smaller scales are resolved, but reduces the accuracy of the model (see, e.g. (3)) .  \nLately, attention has been paid to employing machine learning (ML) methods to leverage high-fidelity data from LES, DNS, and experiments, improving the accuracy ofRANS models while adding minimal cost to the computation (4) . In many ways this is a natural problem for the application of machine learning due to the large number of parameters and non-linear nature of the required model (5) . Two broad strategies can be identified within these works: one approach is to learn a modified Reynolds stress tensor directly from the high-fidelity data, concentrating on regions where certain assumptions of the RANS results break down. This could be done through a neural network, for instance Frey et al. (6) and Ling (7) used neural networks trained on DNS data to correct the eddy viscosity term in the  \nBoussinesq equation. Weatheritt and Sandberg (8) employed Gene Expression Programming (GEP), in which the explicit algebraic Reynolds stress (EASM) framework of Pope (9) was used to perform a symbolic regression to learn improved nonlinear expressions for the anisotropy. The explicit expressions that this approach provides are more interpretable than a neural network, but this is at the expense of degrees of freedom in the model.  \nAn alternative strategy is to modify the RANS turbulence equations to include a spatial correctio","cbCaigA2P1YtxLsG","https://ap.wps.com/l/cbCaigA2P1YtxLsG","pdf",4205187,1,22,"English","en",105,"# Introduction\n## RANS limitations and motivation for ML corrections\n## Two strategies: direct stress learning vs spatial correction/inversion\n## Research challenges and proposed probabilistic framework","[{\"question\":\"What problem does the paper address in turbulence modelling with machine learning?\",\"answer\":\"It targets two difficulties: achieving generalisation to unseen geometries and flow conditions, and efficiently handling heterogeneous datasets that combine experimental and simulation data.\"},{\"question\":\"How does the proposed method improve the k-ω SST RANS turbulence model?\",\"answer\":\"It augments the model with a learned correction function obtained using field inversion together with an ensemble of Gaussian Process Emulators.\"},{\"question\":\"How does the method behave when flow regions are outside the training data physics?\",\"answer\":\"The ensemble uncertainty indicates out-of-distribution regions, leading the corrected simulation to revert to the uncorrected baseline model where physics lies beyond the training set.\"}]","Probabilistic Machine Learning to Improve Generalisation of Data-Driven Turbulence Modelling - A Preprint | PDF",1785811705,55,{"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},"probabilistic-machine-learning-to-improve-generalisation-of-data-driven-turbulence-modelling-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/probabilistic-machine-learning-to-improve-generalisation-of-data-driven-turbulence-modelling-a-preprint/122607/",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","2026-08-04",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 paper address in turbulence modelling with machine learning?","Question",{"text":75,"@type":76},"It targets two difficulties: achieving generalisation to unseen geometries and flow conditions, and efficiently handling heterogeneous datasets that combine experimental and simulation data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method improve the k-ω SST RANS turbulence model?",{"text":80,"@type":76},"It augments the model with a learned correction function obtained using field inversion together with an ensemble of Gaussian Process Emulators.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the method behave when flow regions are outside the training data physics?",{"text":84,"@type":76},"The ensemble uncertainty indicates out-of-distribution regions, leading the corrected simulation to revert to the uncorrected baseline model where physics lies beyond the training set.","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"]