Year: 2021
Author: Carlos A. Michelén Ströfer, Xin-Lei Zhang, Heng Xiao
Communications in Computational Physics, Vol. 30 (2021), Iss. 5 : pp. 1269–1289
Abstract
Training 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0082
Communications in Computational Physics, Vol. 30 (2021), Iss. 5 : pp. 1269–1289
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Ensemble methods turbulence modeling deep learning.
Author Details
-
Data-driven turbulence modeling in separated flows considering physical mechanism analysis
Yan, Chongyang | Li, Haoran | Zhang, Yufei | Chen, HaixinInternational Journal of Heat and Fluid Flow, Vol. 96 (2022), Iss. P.109004
https://doi.org/10.1016/j.ijheatfluidflow.2022.109004 [Citations: 17] -
Explainability analysis of neural network-based turbulence modeling for transonic axial compressor rotor flows
Wu, Chutian | Wang, Shizhao | Zhang, Xin-Lei | He, GuoweiAerospace Science and Technology, Vol. 141 (2023), Iss. P.108542
https://doi.org/10.1016/j.ast.2023.108542 [Citations: 8] -
Optimal sensor placement for ensemble-based data assimilation using gradient-weighted class activation mapping
Xu, Zhaoyue | Wang, Shizhao | Zhang, Xin-Lei | He, GuoweiJournal of Computational Physics, Vol. 514 (2024), Iss. P.113224
https://doi.org/10.1016/j.jcp.2024.113224 [Citations: 1] -
Physical interpretation of neural network-based nonlinear eddy viscosity models
Zhang, Xin-Lei | Xiao, Heng | Jee, Solkeun | He, GuoweiAerospace Science and Technology, Vol. 142 (2023), Iss. P.108632
https://doi.org/10.1016/j.ast.2023.108632 [Citations: 6] -
A PDE-free, neural network-based eddy viscosity model coupled with RANS equations
Xu, Ruiying | Zhou, Xu-Hui | Han, Jiequn | Dwight, Richard P. | Xiao, HengInternational Journal of Heat and Fluid Flow, Vol. 98 (2022), Iss. P.109051
https://doi.org/10.1016/j.ijheatfluidflow.2022.109051 [Citations: 4] -
Data augmented turbulence modeling for three-dimensional separation flows
Yan, Chongyang | Zhang, Yufei | Chen, HaixinPhysics of Fluids, Vol. 34 (2022), Iss. 7
https://doi.org/10.1063/5.0097438 [Citations: 20] -
Combining direct and indirect sparse data for learning generalizable turbulence models
Zhang, Xin-Lei | Xiao, Heng | Luo, Xiaodong | He, GuoweiJournal of Computational Physics, Vol. 489 (2023), Iss. P.112272
https://doi.org/10.1016/j.jcp.2023.112272 [Citations: 11] -
A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers
Wang, Zhiyuan | Zhang, WeiweiPhysics of Fluids, Vol. 35 (2023), Iss. 2
https://doi.org/10.1063/5.0136420 [Citations: 18] -
Ensemble Kalman method for learning turbulence models from indirect observation data
Zhang, Xin-Lei | Xiao, Heng | Luo, Xiaodong | He, GuoweiJournal of Fluid Mechanics, Vol. 949 (2022), Iss.
https://doi.org/10.1017/jfm.2022.744 [Citations: 39] -
Data augmented prediction of Reynolds stresses for flows around an axisymmetric body of revolution
Liu, Yi | Wang, Shizhao | Zhang, Xin-Lei | He, GuoweiOcean Engineering, Vol. 296 (2024), Iss. P.116717
https://doi.org/10.1016/j.oceaneng.2024.116717 [Citations: 0]