Ensemble Gradient for Learning Turbulence Models from Indirect Observations

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dc.contributor.authorStrofer, Carlos A. Michelenen
dc.contributor.authorZhang, Xin-Leien
dc.contributor.authorXiao, Hengen
dc.date.accessioned2022-02-15T14:13:47Zen
dc.date.available2022-02-15T14:13:47Zen
dc.date.issued2021-11-01en
dc.date.updated2022-02-15T14:13:44Zen
dc.description.abstractTraining data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations. A deep neural network representing the turbulence model is trained using the network’s gradients obtained by backpropagation and the ensemble approximation of the RANS sensitivities. Different ensemble approximations are explored and a method based on explicit projection onto the sample space is presented. As validation, the gradient approximations from the different methods are compared to that from the continuous adjoint equations. The ensemble approximation is then used to learn different turbulence models from velocity observations. In all cases, the learned model predicts improved velocities. However, it was observed that once the sensitivity of the velocity to the underlying model becomes small, the approximate nature of the ensemble gradient hinders further optimization of the underlying model. The benefits and limitations of the ensemble gradient approximation are discussed, in particular as compared to the adjoint equations.en
dc.description.versionAccepted versionen
dc.format.extentPages 1269-1289en
dc.format.extent21 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.4208/cicp.OA-2021-0082en
dc.identifier.eissn1991-7120en
dc.identifier.issn1815-2406en
dc.identifier.issue5en
dc.identifier.orcidXiao, Heng [0000-0002-3323-4028]en
dc.identifier.urihttp://hdl.handle.net/10919/108365en
dc.identifier.volume30en
dc.language.isoenen
dc.publisherGlobal Science Pressen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000711870700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPhysics, Mathematicalen
dc.subjectPhysicsen
dc.subjectEnsemble methodsen
dc.subjectturbulence modelingen
dc.subjectdeep learningen
dc.subjectDATA ASSIMILATIONen
dc.subjectKALMAN FILTERen
dc.subjectFORMULATIONen
dc.subjectFLOWSen
dc.subjectApplied Mathematicsen
dc.titleEnsemble Gradient for Learning Turbulence Models from Indirect Observationsen
dc.title.serialCommunications in Computational Physicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/Aerospace and Ocean Engineeringen
pubs.organisational-group/Virginia Tech/University Research Institutesen
pubs.organisational-group/Virginia Tech/University Research Institutes/Fralin Life Sciencesen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen
pubs.organisational-group/Virginia Tech/University Research Institutes/Fralin Life Sciences/Durelle Scotten

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