Sub-grid scale model classification and blending through deep learning

Maulik, Romit; San, Omer; Jacob, Jamey D.; Crick, Christopher

doi:10.1017/jfm.2019.254

Title: Sub-grid scale model classification and blending through deep learning

Journal Article · 14 May 2019 · Journal of Fluid Mechanics

DOI: https://doi.org/10.1017/jfm.2019.254 · OSTI ID:1593562

Maulik, Romit ^[1];

^[2]; Jacob, Jamey D. ^[2]; Crick, Christopher ^[2]

Oklahoma State Univ., Stillwater, OK (United States); Oklahoma State University Stillwater
Oklahoma State Univ., Stillwater, OK (United States)

In this article we detail the use of machine learning for spatio-temporally dynamic turbulence model classification and hybridization for large eddy simulations (LES) of turbulence. Here, our predictive framework is devised around the determination of local conditional probabilities for turbulence models that have varying underlying hypotheses. As a first deployment of this learning, we classify a point on our computational grid as that which requires the functional hypothesis, the structural hypothesis or no modelling at all. This ensures that the appropriate model is specified from a priori knowledge and an efficient balance of model characteristics is obtained in a particular flow computation. In addition, we also utilize the conditional-probability predictions of the same machine learning to blend turbulence models for another hybrid closure. Our test case for the demonstration of this concept is given by Kraichnan turbulence, which exhibits a strong interplay of enstrophy and energy cascades in the wavenumber domain. Our results indicate that the proposed methods lead to robust and stable closure and may potentially be used to combine the strengths of various models for complex flow phenomena prediction.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oklahoma State Univ., Stillwater, OK (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: SC0019290

OSTI ID:: 1593562

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 870; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

References (70)

Evaluation of scale-aware subgrid mesoscale eddy models in a global eddy-rich model Pearson, Brodie; Fox-Kemper, Baylor; Bachman, Scott Ocean Modelling, Vol. 115 https://doi.org/10.1016/j.ocemod.2017.05.007	journal	July 2017
Neural Network Modeling for Near Wall Turbulent Flow Milano, Michele; Koumoutsakos, Petros Journal of Computational Physics, Vol. 182, Issue 1 https://doi.org/10.1006/jcph.2002.7146	journal	October 2002
Structure functions in two-dimensional turbulence Grossmann, Siegfried; Mertens, Peter Zeitschrift für Physik B Condensed Matter, Vol. 88, Issue 1 https://doi.org/10.1007/BF01573844	journal	February 1992
Mathematical Perspectives on Large Eddy Simulation Models for Turbulent Flows Guermond, J. -L.; Oden, J. T.; Prudhomme, S. Journal of Mathematical Fluid Mechanics, Vol. 6, Issue 2 https://doi.org/10.1007/s00021-003-0091-5	journal	June 2004
Smagorinsky constant in LES modeling of anisotropic MHD turbulence Vorobev, Anatoliy; Zikanov, Oleg Theoretical and Computational Fluid Dynamics, Vol. 22, Issue 3-4 https://doi.org/10.1007/s00162-007-0064-z	journal	September 2007
Generalized Deconvolution Procedure for Structural Modeling of Turbulence San, Omer; Vedula, Prakash Journal of Scientific Computing, Vol. 75, Issue 2 https://doi.org/10.1007/s10915-017-0583-8	journal	October 2017
Multilayer feedforward networks are universal approximators Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert Neural Networks, Vol. 2, Issue 5 https://doi.org/10.1016/0893-6080(89)90020-8	journal	January 1989
Neural networks based subgrid scale modeling in large eddy simulations Sarghini, F.; de Felice, G.; Santini, S. Computers & Fluids, Vol. 32, Issue 1 https://doi.org/10.1016/S0045-7930(01)00098-6	journal	January 2003
Two-dimensional turbulence: a physicist approach Tabeling, P. Physics Reports, Vol. 362, Issue 1 https://doi.org/10.1016/S0370-1573(01)00064-3	journal	May 2002
A simple and stable scale-similarity model for large Eddy simulation: Energy balance and existence of weak solutions Layton, W.; Lewandowski, R. Applied Mathematics Letters, Vol. 16, Issue 8 https://doi.org/10.1016/S0893-9659(03)90118-2	journal	November 2003
Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates Lapeyre, Corentin J.; Misdariis, Antony; Cazard, Nicolas Combustion and Flame, Vol. 203 https://doi.org/10.1016/j.combustflame.2019.02.019	journal	May 2019
High-order methods for decaying two-dimensional homogeneous isotropic turbulence San, Omer; Staples, Anne E. Computers & Fluids, Vol. 63 https://doi.org/10.1016/j.compfluid.2012.04.006	journal	June 2012
A stable and scale-aware dynamic modeling framework for subgrid-scale parameterizations of two-dimensional turbulence Maulik, Romit; San, Omer Computers & Fluids, Vol. 158 https://doi.org/10.1016/j.compfluid.2016.11.015	journal	November 2017
A turbulent heat flux prediction framework based on tensor representation theory and machine learning Sotgiu, C.; Weigand, B.; Semmler, K. International Communications in Heat and Mass Transfer, Vol. 95 https://doi.org/10.1016/j.icheatmasstransfer.2018.04.005	journal	July 2018
The development of algebraic stress models using a novel evolutionary algorithm Weatheritt, J.; Sandberg, R. D. International Journal of Heat and Fluid Flow, Vol. 68 https://doi.org/10.1016/j.ijheatfluidflow.2017.09.017	journal	December 2017
A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation Habisreutinger, Marc A.; Bouffanais, Roland; Leriche, Emmanuel Journal of Computational Physics, Vol. 224, Issue 1 https://doi.org/10.1016/j.jcp.2007.02.010	journal	May 2007
Machine learning strategies for systems with invariance properties Ling, Julia; Jones, Reese; Templeton, Jeremy Journal of Computational Physics, Vol. 318 https://doi.org/10.1016/j.jcp.2016.05.003	journal	August 2016
Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach Xiao, H.; Wu, J. -L.; Wang, J. -X. Journal of Computational Physics, Vol. 324 https://doi.org/10.1016/j.jcp.2016.07.038	journal	November 2016
A novel evolutionary algorithm applied to algebraic modifications of the RANS stress–strain relationship Weatheritt, Jack; Sandberg, Richard Journal of Computational Physics, Vol. 325 https://doi.org/10.1016/j.jcp.2016.08.015	journal	November 2016
Deep neural networks for data-driven LES closure models Beck, Andrea; Flad, David; Munz, Claus-Dieter Journal of Computational Physics, Vol. 398 https://doi.org/10.1016/j.jcp.2019.108910	journal	December 2019
Approximate deconvolution large eddy simulation of a barotropic ocean circulation model San, Omer; Staples, Anne E.; Wang, Zhu Ocean Modelling, Vol. 40, Issue 2 https://doi.org/10.1016/j.ocemod.2011.08.003	journal	January 2011
Evaluation of scale-aware subgrid mesoscale eddy models in a global eddy-rich model Pearson, Brodie; Fox-Kemper, Baylor; Bachman, Scott Ocean Modelling, Vol. 115 https://doi.org/10.1016/j.ocemod.2017.05.007	journal	July 2017
Turbulence: The Legacy of A. N. Kolmogorov Frisch, Uriel https://doi.org/10.1017/CBO9781139170666	book	January 1996
The vortices of two-dimensional turbulence Mcwilliams, James C. Journal of Fluid Mechanics, Vol. 219, Issue -1 https://doi.org/10.1017/S0022112090002981	journal	October 1990
Optimal LES formulations for isotropic turbulence Langford, Jacob A.; Moser, Robert D. Journal of Fluid Mechanics, Vol. 398 https://doi.org/10.1017/S0022112099006369	journal	November 1999
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy Journal of Fluid Mechanics, Vol. 807 https://doi.org/10.1017/jfm.2016.615	journal	October 2016
A neural network approach for the blind deconvolution of turbulent flows Maulik, R.; San, O. Journal of Fluid Mechanics, Vol. 831 https://doi.org/10.1017/jfm.2017.637	journal	October 2017
Subgrid modelling for two-dimensional turbulence using neural networks Maulik, R.; San, O.; Rasheed, A. Journal of Fluid Mechanics, Vol. 858 https://doi.org/10.1017/jfm.2018.770	journal	November 2018
Super-resolution reconstruction of turbulent flows with machine learning Fukami, Kai; Fukagata, Koji; Taira, Kunihiko Journal of Fluid Mechanics, Vol. 870 https://doi.org/10.1017/jfm.2019.238	journal	May 2019
An explicit filtering method for large eddy simulation of compressible flows Mathew, Joseph; Lechner, Richard; Foysi, Holger Physics of Fluids, Vol. 15, Issue 8 https://doi.org/10.1063/1.1586271	journal	August 2003
Diffusion Approximation for Two-Dimensional Turbulence Leith, C. E. Physics of Fluids, Vol. 11, Issue 3 https://doi.org/10.1063/1.1691968	journal	January 1968
Inertial Ranges in Two-Dimensional Turbulence Kraichnan, Robert H. Physics of Fluids, Vol. 10, Issue 7 https://doi.org/10.1063/1.1762301	journal	January 1967
An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications Vreman, A. W. Physics of Fluids, Vol. 16, Issue 10 https://doi.org/10.1063/1.1785131	journal	October 2004
Theoretically based optimal large-eddy simulation Moser, Robert D.; Malaya, Nicholas P.; Chang, Henry Physics of Fluids, Vol. 21, Issue 10 https://doi.org/10.1063/1.3249754	journal	October 2009
Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction Hickel, Stefan; Egerer, Christian P.; Larsson, Johan Physics of Fluids, Vol. 26, Issue 10 https://doi.org/10.1063/1.4898641	journal	October 2014
The similarity subgrid stresses associated to the approximate Van Cittert deconvolutions Germano, M. Physics of Fluids, Vol. 27, Issue 3 https://doi.org/10.1063/1.4915620	journal	March 2015
A framework for large eddy simulation of Burgers turbulence based upon spatial and temporal statistical information LaBryer, A.; Attar, P. J.; Vedula, P. Physics of Fluids, Vol. 27, Issue 3 https://doi.org/10.1063/1.4916132	journal	March 2015
Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty Ling, J.; Templeton, J. Physics of Fluids, Vol. 27, Issue 8 https://doi.org/10.1063/1.4927765	journal	August 2015
Dynamic optimization methodology based on subgrid-scale dissipation for large eddy simulation Yu, Changping; Xiao, Zuoli; Li, Xinliang Physics of Fluids, Vol. 28, Issue 1 https://doi.org/10.1063/1.4940044	journal	January 2016
Using field inversion to quantify functional errors in turbulence closures Singh, Anand Pratap; Duraisamy, Karthik Physics of Fluids, Vol. 28, Issue 4 https://doi.org/10.1063/1.4947045	journal	April 2016
Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation Wang, Zhuo; Luo, Kun; Li, Dong Physics of Fluids, Vol. 30, Issue 12 https://doi.org/10.1063/1.5054835	journal	December 2018
Machine learning methods for turbulence modeling in subsonic flows around airfoils Zhu, Linyang; Zhang, Weiwei; Kou, Jiaqing Physics of Fluids, Vol. 31, Issue 1 https://doi.org/10.1063/1.5061693	journal	January 2019
Data-driven deconvolution for large eddy simulations of Kraichnan turbulence Maulik, R.; San, O.; Rasheed, A. Physics of Fluids, Vol. 30, Issue 12 https://doi.org/10.1063/1.5079582	journal	December 2018
A dynamic subgrid‐scale eddy viscosity model Germano, Massimo; Piomelli, Ugo; Moin, Parviz Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7 https://doi.org/10.1063/1.857955	journal	July 1991
A proposed modification of the Germano subgrid‐scale closure method Lilly, D. K. Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 3 https://doi.org/10.1063/1.858280	journal	March 1992
Determination of the Smagorinsky–Lilly constant CS Canuto, V. M.; Cheng, Y. Physics of Fluids, Vol. 9, Issue 5 https://doi.org/10.1063/1.869251	journal	May 1997
An approximate deconvolution procedure for large-eddy simulation Stolz, S.; Adams, N. A. Physics of Fluids, Vol. 11, Issue 7 https://doi.org/10.1063/1.869867	journal	July 1999
A dynamic eddy-viscosity closure model for large eddy simulations of two-dimensional decaying turbulence San, O. International Journal of Computational Fluid Dynamics, Vol. 28, Issue 6-10 https://doi.org/10.1080/10618562.2014.948426	journal	June 2014
A dynamic framework for functional parameterisations of the eddy viscosity coefficient in two-dimensional turbulence Maulik, R.; San, O. International Journal of Computational Fluid Dynamics, Vol. 31, Issue 2 https://doi.org/10.1080/10618562.2017.1287902	journal	February 2017
Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures Vollant, A.; Balarac, G.; Corre, C. Journal of Turbulence, Vol. 18, Issue 9 https://doi.org/10.1080/14685248.2017.1334907	journal	June 2017
Two-dimensional turbulence Kraichnan, R. H.; Montgomery, D. Reports on Progress in Physics, Vol. 43, Issue 5 https://doi.org/10.1088/0034-4885/43/5/001	journal	May 1980
Ten questions concerning the large-eddy simulation of turbulent flows Pope, Stephen B. New Journal of Physics, Vol. 6 https://doi.org/10.1088/1367-2630/6/1/035	journal	January 2004
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data Wang, Jian-Xun; Wu, Jin-Long; Xiao, Heng Physical Review Fluids, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevFluids.2.034603	journal	March 2017
Searching for turbulence models by artificial neural network Gamahara, Masataka; Hattori, Yuji Physical Review Fluids, Vol. 2, Issue 5 https://doi.org/10.1103/PhysRevFluids.2.054604	journal	May 2017
Log-Normal Turbulence Dissipation in Global Ocean Models Pearson, Brodie; Fox-Kemper, Baylor Physical Review Letters, Vol. 120, Issue 9 https://doi.org/10.1103/PhysRevLett.120.094501	journal	February 2018
Turbulence Modeling in the Age of Data Duraisamy, Karthik; Iaccarino, Gianluca; Xiao, Heng Annual Review of Fluid Mechanics, Vol. 51, Issue 1 https://doi.org/10.1146/annurev-fluid-010518-040547	journal	January 2019
Two-Dimensional Turbulence Boffetta, Guido; Ecke, Robert E. Annual Review of Fluid Mechanics, Vol. 44, Issue 1 https://doi.org/10.1146/annurev-fluid-120710-101240	journal	January 2012
General Circulation Experiments with the Primitive Equations: i. the Basic Experiment* Smagorinsky, J. Monthly Weather Review, Vol. 91, Issue 3 https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2	journal	March 1963
Hybrid Reynolds-Averaged/Large-Eddy Simulation Methodology from Symbolic Regression: Formulation and Application Weatheritt, Jack; Sandberg, Richard D. AIAA Journal, Vol. 55, Issue 11 https://doi.org/10.2514/1.J055378	journal	November 2017
Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils Singh, Anand Pratap; Medida, Shivaji; Duraisamy, Karthik AIAA Journal, Vol. 55, Issue 7 https://doi.org/10.2514/1.J055595	journal	July 2017
Improved subgrid-scale models for large-eddy simulation Bardina, J.; Ferziger, J.; Reynolds, W. 13th Fluid and PlasmaDynamics Conference https://doi.org/10.2514/6.1980-1357	conference	February 2013
A Machine Learning Strategy to Assist Turbulence Model Development Tracey, Brendan D.; Duraisamy, Karthikeyan; Alonso, Juan J. 53rd AIAA Aerospace Sciences Meeting https://doi.org/10.2514/6.2015-1287	conference	January 2015
Data-driven Adaptive Physics Modeling for Turbulence Simulations Ling, Julia; Kurzawski, Andrew 23rd AIAA Computational Fluid Dynamics Conference https://doi.org/10.2514/6.2017-3627	conference	June 2017
Approximate deconvolution large eddy simulation of a barotropic ocean circulation model San, Omer; Staples, Anne E.; Wang, Zhu arXiv https://doi.org/10.48550/arxiv.1104.2730	text	January 2011
High-order methods for decaying two-dimensional homogeneous isotropic turbulence San, Omer; Staples, Anne E. arXiv https://doi.org/10.48550/arxiv.1212.0920	text	January 2012
Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach Xiao, H.; Wu, J. -L.; Wang, J. -X. arXiv https://doi.org/10.48550/arxiv.1508.06315	text	January 2015
A neural network approach for the blind deconvolution of turbulent flows Maulik, Romit; San, Omer arXiv https://doi.org/10.48550/arxiv.1706.00912	text	January 2017
Generalized deconvolution procedure for structural modeling of turbulence San, Omer; Vedula, Prakash arXiv https://doi.org/10.48550/arxiv.1707.09177	preprint	January 2017
Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates Lapeyre, C. J.; Misdariis, A.; Cazard, N. arXiv https://doi.org/10.48550/arxiv.1810.03691	text	January 2018
Data-driven deconvolution for large eddy simulations of Kraichnan turbulence Maulik, Romit; San, Omer; Rasheed, Adil arXiv https://doi.org/10.48550/arxiv.1812.02211	preprint	January 2018

Cited By (2)

Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data Vaddireddy, Harsha; Rasheed, Adil; Staples, Anne E. Physics of Fluids, Vol. 32, Issue 1 https://doi.org/10.1063/1.5136351	journal	January 2020
Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network Xie, Chenyue; Li, Ke; Ma, Chao Physical Review Fluids, Vol. 4, Issue 10 https://doi.org/10.1103/physrevfluids.4.104605	journal	October 2019

Similar Records

Spatiotemporally dynamic implicit large eddy simulation using machine learning classifiers

Journal Article · 2020 · Physica. D, Nonlinear Phenomena · OSTI ID:1737502

Maulik, Romit; San, Omer; Jacob, Jamey D.

Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows

Journal Article · 2021 · Physical Review Fluids (Online) · OSTI ID:1853026

Pawar, Suraj; San, Omer

Subgrid modelling for two-dimensional turbulence using neural networks

Journal Article · 2019 · Journal of Fluid Mechanics · OSTI ID:1593570

Maulik, R.; San, O.; Rasheed, A.; +1 more

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Mathematical Foundations: Computational methods
Turbulent Flows: Turbulence modelling

Title: Sub-grid scale model classification and blending through deep learning

Citation Formats

References (70)

Cited By (2)

Similar Records

Related Subjects