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A supervised k-nearest neighbors regressor combined with a Gaussian process learns statistical features from experimental data and predicts mean flow and turbulent fluctuations. The framework is validated by comparing predicted trajectories with extensive Lagrangian particle tracking measurements across flow conditions. Agreement is shown for local velocity distributions, Lagrangian statistics, solid concentration distributions, and phase flow numbers, demonstrating accurate, efficient, robust modeling with minimal driver data. ","University of Birmingham  \nA data-driven machine learning framework for modelling of turbulent mixing flows  \nLi, Kun; Savari, Chiya; Sheikh, Hamzah; Barigou, Mostafa  \nDOI:  \n10.1063/5.0136830  \nLicense:  \nCreative Commons: Attribution (CC BY)  \nDocument Version  \nPublisher's PDF, also known as Version of record  \nCitation for published version (Harvard):  \nLi, K, Savari, C, Sheikh, H & Barigou, M 2023, 'A data-driven machine learning framework for modelling of turbulent mixing flows', Physics of Fluids, vol. 35, 015150. [https://doi.org/10.1063/5.0136830](https://doi.org/10.1063/5.0136830)  \nLink to publication on Research at Birmingham portal  \nGeneral rights  \nUnless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or the copyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposes permitted by law.  \n•Users may freely distribute the URL that is used to identify this publication.  \n•Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of private study or non-commercial research.  \n•User may use extracts from the document in line with the concept of ‘fair dealing’ under the Copyright, Designs and Patents Act 1988 (?)  \n•Users may not further distribute the material nor use it for the purposes of commercial gain.  \nWhere a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.  \nWhen citing, please reference the published version.  \nTake down policy  \nWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.  \nIf you believe that this is the case for this document, [please contact UBIRA@lists.bham.ac.uk](please contact UBIRA@lists.bham.ac.uk) providing details and we will remove access to the work immediately and investigate.  \nDownload date: 05. Aug. 2026  \nA data-driven machine learning framework for modeling of turbulent mixing flows  \n\n| Cite as: Phys. Fluids 35, 015150 (2023); [https://doi.org/10.1063/5.0136830](https://doi.org/10.1063/5.0136830)\u003Cbr>Submitted: 29 November 2022 • Accepted: 03 January 2023 • Accepted Manuscript Online: 04 January 2023 • Published Online: 24 January 2023\u003Cbr>Published open access through an agreement with JISC Collections |  |  |  |\n| --- | --- | --- | --- |\n|  Kun Li (李坤),  Chiya Savari, Hamzah A. Sheikh, et al. |  |  |  |\n| COLLECTIONS\u003Cbr>Paper published as part of the special topic on Multiphase flow in energy studies and applications: A special issue for MTCUE-2022 |  |  |  |\n|  |  |  |  |\n\nARTICLES YOU MAY BE INTERESTED IN  \nLagrangian wavelet analysis of turbulence modulation in particle–liquid mixing flows Physics of Fluids 34, 115121 (2022); [https://doi.org/10.1063/5.0127698](https://doi.org/10.1063/5.0127698)  \n[Linear attention coupled Fourier neural operator for simulation of three-dimensional](Linear attention coupled Fourier neural operator for simulation of three-dimensional)[ ](Linear attention coupled Fourier neural operator for simulation of three-dimensional)turbulence  \nPhysics of Fluids 35, 015106 (2023); [https://doi.org/10.1063/5.0130334](https://doi.org/10.1063/5.0130334)  \nPhysics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations Physics of Fluids 34, 075117 (2022); [https://doi.org/10.1063/5.0095270](https://doi.org/10.1063/5.0095270)  \nPhys. Fluids 35, 015150 (2023); [https://doi.org/10.1063/5.0136830](https://doi.org/10.1063/5.0136830) 35, 015150  \n© 2023 Author(s) .  \nPhysics of Fluids ARTICLE  \n[scitation.org/journal/phf](scitation.org/journal/phf)  \nA data-driven machine learning framework for modeling of turbulent mixing flows  \n\n| Cite as: Phys. Fluids 35, 015150 (2023); doi: 10.1063/5.013683","cbCaigssqnGjwqDP","https://ap.wps.com/l/cbCaigssqnGjwqDP","pdf",7108253,2,1,18,"English","en",105,"# Abstract\n## ML framework for turbulent flow-field reconstruction\n## Learning method and prediction targets\n## Validation against Lagrangian particle tracking\n## Agreement metrics and practical implications","[{\"question\":\"What input data does the proposed ML framework require?\",\"answer\":\"It uses a very short-term experimental Lagrangian trajectory as driver data to construct turbulent flow fields.\"},{\"question\":\"How does the framework model turbulent flows?\",\"answer\":\"It combines a supervised k-nearest neighbors regressor with a Gaussian process, sharing statistical features learned from experimental data to predict mean flow and turbulent fluctuations.\"},{\"question\":\"How is the framework evaluated and how accurate is it?\",\"answer\":\"Predicted trajectories are compared with extensive Lagrangian particle tracking measurements under various flow conditions, showing very good agreement in velocity distributions, Lagrangian statistics, solid concentration distributions, and phase flow numbers.\"}]","A data-driven machine learning framework for modelling of turbulent mixing flows | 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