[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123725-en":3,"doc-seo-123725-105":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},123725,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers","A novel unsupervised machine-learning shock sensor is presented for high-order supersonic flow solvers, built on Gaussian Mixture Models (GMMs). The GMM sensor delivers high accuracy in detecting shocks and remains robust across diverse test cases while requiring significantly less parameter tuning than competing approaches. It is integrated into a high-order compressible discontinuous Galerkin solver, coupling with two stabilization strategies. Validation on Sedov blast and double Mach reflection improves hybrid sub-cell flux-differencing, while supersonic high-Reynolds tests enable entropy-stable artificial viscosity with comparable effectiveness. Its adaptive, training-free design supports complex geometries and varied flow configurations, enhancing robustness and efficiency in advanced CFD codes.","An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers  \narXiv :2308 .00086v 3 [ cs .LG] 9 Oct 2023  \nAndr´es Mateo-Gab´ın,1, a) Kenza Tlales,1 Eusebio Valero,1, 2 Esteban Ferrer,1, 2 and Gonzalo Rubio1, 2  \n1) ETSIAE-UPM-School of Aeronautics, Universidad Polit´ecnica de Madrid, Madrid-Spain  \n2) Center for Computational Simulation, Universidad Polit´ecnica de Madrid, Madrid-Spain (Dated: 10 October 2023)  \nWe present a novel unsupervised machine-learning sock sensor based on Gaussian Mixture Models (GMMs) . The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases with significantly less parameter tuning than other options. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver, where two stabilization approaches are coupled to the sensor to provide examples of possible applications. The Sedov blast and double Mach reflection cases demonstrate that our proposed sensor can enhance hybrid sub-cell flux-differencing formulations by providing accurate information of the nodes that require low-order blending. Besides, supersonic test cases including high Reynolds numbers showcase the sensor performance when used to introduce entropy-stable artificial viscosity to capture shocks, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine-learning methods, exemplified by this GMM sensor, to improve the robustness and efficiency of advanced CFD codes.  \nI. INTRODUCTION  \nShock waves are complex and significant fluid phenomena in engineering, observed, for example, in high-speed transport or in combustion and detonation processes.1 High-speed flows exhibit a combination of smooth regions and thin regions with abrupt changes in flow properties. To effectively handle the various scales present in these flows, it is necessary to employ robust and computationally efficient numerical schemes that maintain a high level of precision.2 Standard discretizations for smooth flows may exhibit oscillations when shocks are present, and require special techniques for shock regularization within designated regions.2  \nThe shock-fitting approach, which explicitly tracks and fits shock waves, is one method used to handle shocks.3–5 However, the utilization of shock fitting is limited, primarily due to the difficulties it presents when applied to unstructured grids. An alternative and more commonly employed approach is the use of shock-capturing methods. The choice of the baseline discretization scheme determines the availability of various shock-capturing approaches. For finite volume discretizations,6 typical options include TVD limiting strategies7 or essentially nonoscillatory (W)ENO reconstructions.8–14 In the case of flux reconstruction (FR) 15,16 and discontinuous Galerkin (DG) 17 schemes, the methods generally fall into two categories. The first category involves the local switching of the discretization operator to a more robust one, achieved through h-refinement and/or p-coarsening. By employing appropriate limiting techniques, this operator ensures both accuracy and solution boundedness.18–28 A simi-  \na) Electronic mail: andres.mgabin@upm.es.  \nlar approach involves performing a hybrid blending with a low-order sub-cell variant of the scheme.29–32 In the second category, known as the artificial viscosity shockcapturing method, a local diffusion operator with a predetermined strength is introduced to regularize the solution once a shock is detected.33–43  \nRegardless of the specific method used, accurately determining the precise location of shock waves is of paramount importance. This becomes particularly cr","cbCaiecvtgCof3cI","https://ap.wps.com/l/cbCaiecvtgCof3cI","pdf",14396297,1,29,"English","en",105,"# Introduction\n## Shock waves and numerical challenges\n## Shock-capturing methods and sensors\n## Machine learning for shock detection","[{\"question\":\"What sensor approach is proposed for high-order supersonic flow solvers?\",\"answer\":\"The work proposes an unsupervised shock sensor based on Gaussian Mixture Models (GMMs). The sensor is designed to detect shocks accurately without extensive manual tuning or large training datasets.\"},{\"question\":\"How is the GMM sensor integrated into the numerical solver?\",\"answer\":\"The GMM sensor is coupled to a high-order compressible discontinuous Galerkin (DG) solver. Two stabilization approaches are connected to the sensor to illustrate possible applications.\"},{\"question\":\"What results demonstrate the sensor’s usefulness?\",\"answer\":\"Sedov blast and double Mach reflection cases show improved hybrid sub-cell flux-differencing by identifying nodes needing low-order blending. Supersonic tests with high Reynolds numbers show that the sensor can introduce entropy-stable artificial viscosity with effectiveness comparable to fine-tuned state-of-the-art sensors.\"}]","An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers | PDF",1785818208,73,{"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},"an-unsupervised-machine-learning-based-shock-sensor-for-high-order-supersonic-flow-solvers","",{"@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/an-unsupervised-machine-learning-based-shock-sensor-for-high-order-supersonic-flow-solvers/123725/",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 sensor approach is proposed for high-order supersonic flow solvers?","Question",{"text":75,"@type":76},"The work proposes an unsupervised shock sensor based on Gaussian Mixture Models (GMMs). The sensor is designed to detect shocks accurately without extensive manual tuning or large training datasets.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the GMM sensor integrated into the numerical solver?",{"text":80,"@type":76},"The GMM sensor is coupled to a high-order compressible discontinuous Galerkin (DG) solver. Two stabilization approaches are connected to the sensor to illustrate possible applications.",{"name":82,"@type":73,"acceptedAnswer":83},"What results demonstrate the sensor’s usefulness?",{"text":84,"@type":76},"Sedov blast and double Mach reflection cases show improved hybrid sub-cell flux-differencing by identifying nodes needing low-order blending. Supersonic tests with high Reynolds numbers show that the sensor can introduce entropy-stable artificial viscosity with effectiveness comparable to fine-tuned state-of-the-art sensors.","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"]