[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126893-en":3,"doc-seo-126893-105":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},126893,2336474466712,"Maeve","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine learning-based vorticity evolution and superresolution of homogeneous isotropic turbulence using wavelet projection","A wavelet-based machine learning framework predicts the time evolution of homogeneous isotropic turbulence while preserving vortex-tube structures. Three-dimensional convolutional neural networks together with long short-term memory models are trained using direct numerical simulation time-series data at Taylor-microscale Reynolds number 92. Predictions are evaluated through vorticity flow visualizations and turbulence statistics, including vorticity probability density functions and enstrophy spectra, showing strong agreement with DNS results. The approach also reconstructs small-scale topology using velocity-gradient invariants and enables superresolution of coarse-grained vorticity that regenerates fine-scale information and vortex tubes.","arXiv :2404 .02256v1 [physics .flu-dyn] 2 Apr 2024  \nMachine learning-based vorticity evolution and superresolution of homogeneous isotropic turbulence using wavelet projection  \nTomoki Asaka, 1, a) Katsunori Yoshimatsu∗ ,2, b) and Kai Schneider3, c)  \n1) Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan  \n2) Institute of Materials and Systems for Sustainability, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan  \n3) Institut de Math´ematiques de Marseille (I2M), Aix Marseille Universit´e, CNRS, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France  \n(Dated: 4 April 2024)  \nA wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Threedimensional convolutional neural networks and long short-term memory are trained with a time series of direct numerical simulation (DNS) data of homogeneous isotropic turbulence at the Taylor microscale Reynolds number 92 . The predicted results are assessed by using flow visualization of vorticity and statistics, e.g., probability density functions of vorticity and enstrophy spectra. It is found that the predicted results are in good agreement with DNS results. The small-scale flow topology considering the second and third invariant of the velocity gradient tensor likewise shows an approximate match. Furthermore, we apply the pre-trained neural networks to coarsegrained vorticity data using superresolution. It is shown that the superresolved flow field well agrees with the reference DNS field and thus small-scale information and vortex tubes are well regenerated.  \na) [ask05102569@gmail.com](ask05102569@gmail.com)b)[yoshimatsu@nagoya-u.jp](yoshimatsu@nagoya-u.jp)  \nc) [kai.schneider@univ-amu.fr](kai.schneider@univ-amu.fr)  \nI. INTRODUCTION  \nSelf-organization in small-scale turbulence is ubiquitous for instance in the form of coherent vortex tubes. The vortices defined as regions of intense vorticity magnitude are characteristic at scales in the dissipation range (e.g., Refs. 1 and 2) . They are intermittently distributed in physical space. Moreover, they play key roles for the dynamics of e.g. , inertial particle clustering,3 mixing in combustion,4 and extreme acceleration of fluid particles.5 The representative length scale and time scale are respectively the Kolmogorov length scale η and the Kolmogorov time scale τη . Jim´enez et al. 1 found that the typical diameter of the tubes is about 10η . In turbulence modeling, such as large-eddy simulation, the influence of the vortices is statistically modeled without resolving the scales in the dissipation rage.  \nMachine learning in fluid dynamics is an active rapidly evolving and promising field. For reviews we refer to Refs. 6–8. The increasing power and capabilities of machine learning approaches can provide benefit to in particular computational fluid dynamics. Computationally expensive direct numerical simulation (DNS) computations may thus be reduced or even avoided in the near future by training neural networks with available turbulent flow data.9,10 The application of machine learning covers, e.g. , extraction of flow features, turbulence modeling, superresolution (SR) of unresolved flows, and time-evolution of flows. Among various applications, we focus in the following on SR and predicting the time evolution of flows.  \nSR is not limited to improve the resolution of images.11 Dong et al. 12 proposed a deeplearning SR method, by using convolutional neural networks (CNN) which learn the local area of flow structure via convolution filters. SR using two-dimensional (2D) CNN has been applied to turbulence; 2D freely-decaying homogeneous turbulence, 13 urban turbulence, 14 three-dimensional (3D) forced homogeneous isotropic turbulence (e.g., Refs. 15 and 16), and 3D turbulent channel flows (e.g. , Refs. 15 and 16) . Liu et al. 15 trained velocity fie","cbCaig16MJZg8aUs","https://ap.wps.com/l/cbCaig16MJZg8aUs","pdf",2077226,1,34,"English","en",105,"# Introduction\n## Background: coherent vortex tubes and turbulence modeling\n## Machine learning in fluid dynamics\n## Superresolution methods for turbulence","[{\"question\":\"What is the proposed wavelet-based machine learning approach used for?\",\"answer\":\"It predicts the time evolution of homogeneous isotropic turbulence while preserving vortex tubes, and it also supports superresolution from coarse-grained vorticity data.\"},{\"question\":\"Which neural network architectures are trained in the study?\",\"answer\":\"The method trains 3D convolutional neural networks and long short-term memory models using DNS time-series data.\"},{\"question\":\"How are the predictions validated against DNS data?\",\"answer\":\"Validation uses vorticity visualizations and statistical measures such as vorticity probability density functions and enstrophy spectra, and it also checks small-scale topology via invariants of the velocity-gradient tensor.\"}]","Machine learning-based vorticity evolution and superresolution of homogeneous isotropic turbulence using wavelet projection | 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is the proposed wavelet-based machine learning approach used for?","Question",{"text":75,"@type":76},"It predicts the time evolution of homogeneous isotropic turbulence while preserving vortex tubes, and it also supports superresolution from coarse-grained vorticity data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which neural network architectures are trained in the study?",{"text":80,"@type":76},"The method trains 3D convolutional neural networks and long short-term memory models using DNS time-series data.",{"name":82,"@type":73,"acceptedAnswer":83},"How are the predictions validated against DNS data?",{"text":84,"@type":76},"Validation uses vorticity visualizations and statistical measures such as vorticity probability density functions and enstrophy spectra, and it also checks small-scale topology via invariants of the velocity-gradient 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