A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Rahman, Sk.; San, Omer; Rasheed, Adil

doi:10.3390/fluids3040086

Title: A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Journal Article · Wed Oct 31 00:00:00 EDT 2018 · Fluids

DOI:https://doi.org/10.3390/fluids3040086· OSTI ID:1593573

Rahman, Sk. ^[1];

^[1]; Rasheed, Adil ^[2]

Oklahoma State Univ., Stillwater, OK (United States)
SINTEF Digital, Trondheim (Norway)

We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes. We introduce a weighting parameter between the Galerkin projection and extreme learning machine models and explore its effectiveness, accuracy and generalizability. To illustrate the success of the proposed modeling paradigm, we predict both the mean flow pattern and the time series response of a single-layer quasi-geostrophic ocean model, which is a simplified prototype for wind-driven general circulation models. We demonstrate that our approach yields significant improvements over both the standard Galerkin projection and fully non-intrusive neural network methods with a negligible computational overhead.

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

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

Grant/Contract Number:: SC0019290

OSTI ID:: 1593573

Journal Information:: Fluids, Vol. 3, Issue 4; ISSN 2311-5521

Publisher:: MDPICopyright Statement

Country of Publication:: United States

Language:: English

References (75)

A Reduced-Order Method for Simulation and Control of Fluid Flows Ito, K.; Ravindran, S. S. Journal of Computational Physics, Vol. 143, Issue 2 https://doi.org/10.1006/jcph.1998.5943	journal	July 1998
Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres Kondrashov, Dmitri; Chekroun, Mickaël; Berloff, Pavel Fluids, Vol. 3, Issue 1 https://doi.org/10.3390/fluids3010021	journal	March 2018
Data-assisted reduced-order modeling of extreme events in complex dynamical systems Wan, Zhong Yi; Vlachas, Pantelis; Koumoutsakos, Petros PLOS ONE, Vol. 13, Issue 5 https://doi.org/10.1371/journal.pone.0197704	journal	May 2018
An analysis of numerical issues in neural training by pseudoinversion Cancelliere, R.; Deluca, R.; Gai, M. Computational and Applied Mathematics, Vol. 36, Issue 1 https://doi.org/10.1007/s40314-015-0246-z	journal	June 2015
A reduced-order model for heat transfer in multiphase flow and practical aspects of the proper orthogonal decomposition Brenner, Thomas A.; Fontenot, Raymond L.; Cizmas, Paul G. A. Computers & Chemical Engineering, Vol. 43 https://doi.org/10.1016/j.compchemeng.2012.04.003	journal	August 2012
Renewable energy from the ocean Pelc, Robin; Fujita, Rod M. Marine Policy, Vol. 26, Issue 6 https://doi.org/10.1016/S0308-597X(02)00045-3	journal	November 2002
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
Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model Pathak, Jaideep; Wikner, Alexander; Fussell, Rebeckah Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, Issue 4 https://doi.org/10.1063/1.5028373	journal	April 2018
Current developments and future prospects of offshore wind and ocean energy Esteban, Miguel; Leary, David Applied Energy, Vol. 90, Issue 1 https://doi.org/10.1016/j.apenergy.2011.06.011	journal	February 2012
Mesoscale atmosphere ocean coupling enhances the transfer of wind energy into the ocean Byrne, D.; Münnich, M.; Frenger, I. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms11867	journal	June 2016
Computation of rare transitions in the barotropic quasi-geostrophic equations Laurie, Jason; Bouchet, Freddy New Journal of Physics, Vol. 17, Issue 1 https://doi.org/10.1088/1367-2630/17/1/015009	journal	January 2015
An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD: AN IMPROVED ALGORITHM FOR DYNAMIC MODE DECOMPOSITION VS POD Bistrian, D. A.; Navon, I. M. International Journal for Numerical Methods in Fluids, Vol. 78, Issue 9 https://doi.org/10.1002/fld.4029	journal	April 2015
Application of neural networks to turbulence control for drag reduction Lee, Changhoon; Kim, John; Babcock, David Physics of Fluids, Vol. 9, Issue 6 https://doi.org/10.1063/1.869290	journal	June 1997
Acceleration techniques for reduced-order models based on proper orthogonal decomposition Cizmas, Paul G. A.; Richardson, Brian R.; Brenner, Thomas A. Journal of Computational Physics, Vol. 227, Issue 16 https://doi.org/10.1016/j.jcp.2008.04.036	journal	August 2008
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake Noack, Bernd R.; Afanasiev, Konstantin; MorzyŃSki, Marek Journal of Fluid Mechanics, Vol. 497 https://doi.org/10.1017/S0022112003006694	journal	December 2003
Model Reduction for Flow Analysis and Control Rowley, Clarence W.; Dawson, Scott T. M. Annual Review of Fluid Mechanics, Vol. 49, Issue 1 https://doi.org/10.1146/annurev-fluid-010816-060042	journal	January 2017
The Effects of Mesoscale Ocean–Atmosphere Coupling on the Large-Scale Ocean Circulation Hogg, Andrew Mc C.; Dewar, William K.; Berloff, Pavel Journal of Climate, Vol. 22, Issue 15 https://doi.org/10.1175/2009JCLI2629.1	journal	August 2009
Reduced order models based on local POD plus Galerkin projection Rapún, María-Luisa; Vega, José M. Journal of Computational Physics, Vol. 229, Issue 8 https://doi.org/10.1016/j.jcp.2009.12.029	journal	April 2010
Multilevel Algorithm for Obtaining the Proper Orthogonal Decomposition Behzad, Fariduddin; Helenbrook, Brian T.; Ahmadi, Goodarz AIAA Journal, Vol. 56, Issue 11 https://doi.org/10.2514/1.J056807	journal	November 2018
Emergence of Inertial Gyres in a Two-Layer Quasigeostrophic Ocean Model Özgökmen, Tamay M.; Chassignet, Eric P. Journal of Physical Oceanography, Vol. 28, Issue 3 https://doi.org/10.1175/1520-0485(1998)028<0461:EOIGIA>2.0.CO;2	journal	March 1998
Randomized dynamic mode decomposition for nonintrusive reduced order modelling: RANDOMIZED DYNAMIC MODE DECOMPOSITION FOR NIROM Bistrian, Diana Alina; Navon, Ionel Michael International Journal for Numerical Methods in Engineering, Vol. 112, Issue 1 https://doi.org/10.1002/nme.5499	journal	February 2017
Numerical assessments of ocean energy extraction from western boundary currents using a quasi-geostrophic ocean circulation model San, Omer International Journal of Marine Energy, Vol. 16 https://doi.org/10.1016/j.ijome.2016.05.002	journal	December 2016
Extreme learning machines: a survey Huang, Guang-Bin; Wang, Dian Hui; Lan, Yuan International Journal of Machine Learning and Cybernetics, Vol. 2, Issue 2 https://doi.org/10.1007/s13042-011-0019-y	journal	May 2011
Dynamically consistent parameterization of mesoscale eddies. Part I: Simple model Berloff, Pavel Ocean Modelling, Vol. 87 https://doi.org/10.1016/j.ocemod.2014.12.008	journal	March 2015
Some Recent Developments in Turbulence Closure Modeling Durbin, Paul A. Annual Review of Fluid Mechanics, Vol. 50, Issue 1 https://doi.org/10.1146/annurev-fluid-122316-045020	journal	January 2018
Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions IEEE Transactions on Neural Networks, Vol. 9, Issue 1 https://doi.org/10.1109/72.655045	journal	January 1998
A proper orthogonal decomposition method for nonlinear flows with deforming meshes Freno, Brian A.; Cizmas, Paul G. A. International Journal of Heat and Fluid Flow, Vol. 50 https://doi.org/10.1016/j.ijheatfluidflow.2014.07.001	journal	December 2014
Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison Wang, Zhu; Akhtar, Imran; Borggaard, Jeff Computer Methods in Applied Mechanics and Engineering, Vol. 237-240 https://doi.org/10.1016/j.cma.2012.04.015	journal	September 2012
Numeric sensitivity analysis applied to feedforward neural networks Monta�o, J. J.; Palmer, A. Neural Computing & Applications, Vol. 12, Issue 2 https://doi.org/10.1007/s00521-003-0377-9	journal	November 2003
Numerical Simulations of the Vertical Structure of Quasi-Geostrophic Turbulence Hua, B. L.; Haidvogel, D. B. Journal of the Atmospheric Sciences, Vol. 43, Issue 23 https://doi.org/10.1175/1520-0469(1986)043<2923:NSOTVS>2.0.CO;2	journal	December 1986
Closed-Loop Turbulence Control: Progress and Challenges Brunton, Steven L.; Noack, Bernd R. Applied Mechanics Reviews, Vol. 67, Issue 5 https://doi.org/10.1115/1.4031175	journal	August 2015
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
Modal Analysis of Fluid Flows: An Overview Taira, Kunihiko; Brunton, Steven L.; Dawson, Scott T. M. AIAA Journal, Vol. 55, Issue 12 https://doi.org/10.2514/1.J056060	journal	December 2017
Calibration of POD reduced-order models using Tikhonov regularization Cordier, L.; El Majd, B. Abou; Favier, J. International Journal for Numerical Methods in Fluids https://doi.org/10.1002/fld.2074	journal	January 2009
Convex incremental extreme learning machine Huang, Guang-Bin; Chen, Lei Neurocomputing, Vol. 70, Issue 16-18 https://doi.org/10.1016/j.neucom.2007.02.009	journal	October 2007
Climate dynamics and fluid mechanics: Natural variability and related uncertainties Ghil, Michael; Chekroun, Mickaël D.; Simonnet, Eric Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17 https://doi.org/10.1016/j.physd.2008.03.036	journal	August 2008
Hybrid Reduced-Order Integration with Proper Orthogonal Decomposition and Dynamic Mode Decomposition Williams, Matthew O.; Schmid, Peter J.; Kutz, J. Nathan Multiscale Modeling & Simulation, Vol. 11, Issue 2 https://doi.org/10.1137/120874539	journal	January 2013
Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review] Jang, J. S. R.; Sun, C. T.; Mizutani, E. IEEE Transactions on Automatic Control, Vol. 42, Issue 10 https://doi.org/10.1109/TAC.1997.633847	journal	October 1997
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body Östh, Jan; Noack, Bernd R.; Krajnović, Siniša Journal of Fluid Mechanics, Vol. 747 https://doi.org/10.1017/jfm.2014.168	journal	April 2014
On the sensitivity and accuracy of proper-orthogonal-decomposition-based reduced order models for Burgers equation Behzad, Fariduddin; Helenbrook, Brian T.; Ahmadi, Goodarz Computers & Fluids, Vol. 106 https://doi.org/10.1016/j.compfluid.2014.09.041	journal	January 2015
Sales forecasting using extreme learning machine with applications in fashion retailing Sun, Zhan-Li; Choi, Tsan-Ming; Au, Kin-Fan Decision Support Systems, Vol. 46, Issue 1 https://doi.org/10.1016/j.dss.2008.07.009	journal	December 2008
Reduced-order modeling: new approaches for computational physics Lucia, David J.; Beran, Philip S.; Silva, Walter A. Progress in Aerospace Sciences, Vol. 40, Issue 1-2 https://doi.org/10.1016/j.paerosci.2003.12.001	journal	February 2004
Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I Arakawa, Akio Journal of Computational Physics, Vol. 1, Issue 1 https://doi.org/10.1016/0021-9991(66)90015-5	journal	August 1966
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
On the Wind-Driven Ocean Circulation Munk, Walter H. Journal of Meteorology, Vol. 7, Issue 2 https://doi.org/10.1175/1520-0469(1950)007<0080:OTWDOC>2.0.CO;2	journal	April 1950
Stability Properties of POD-Galerkin Approximations for the Compressible Navier-Stokes Equations Iollo, A.; Lanteri, S.; Désidéri, J. -A. Theoretical and Computational Fluid Dynamics, Vol. 13, Issue 6 https://doi.org/10.1007/s001620050119	journal	March 2000
SUPG reduced order models for convection-dominated convection–diffusion–reaction equations Giere, Swetlana; Iliescu, Traian; John, Volker Computer Methods in Applied Mechanics and Engineering, Vol. 289 https://doi.org/10.1016/j.cma.2015.01.020	journal	June 2015
Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses Berloff, Pavel Fluids, Vol. 1, Issue 3 https://doi.org/10.3390/fluids1030022	journal	June 2016
A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation San, Omer; Iliescu, Traian Advances in Computational Mathematics, Vol. 41, Issue 5 https://doi.org/10.1007/s10444-015-9417-0	journal	May 2015
Turbulence and the dynamics of coherent structures. I. Coherent structures Sirovich, Lawrence Quarterly of Applied Mathematics, Vol. 45, Issue 3 https://doi.org/10.1090/qam/910462	journal	January 1987
Numerical Integration of the Barotropic Vorticity Equation Charney, J. G.; FjÖrtoft, R.; Neumann, J. Von Tellus, Vol. 2, Issue 4 https://doi.org/10.3402/tellusa.v2i4.8607	journal	January 1950
Closed-loop separation control using machine learning Gautier, N.; Aider, J. -L.; Duriez, T. Journal of Fluid Mechanics, Vol. 770 https://doi.org/10.1017/jfm.2015.95	journal	April 2015
Inertial gyres in decaying and forced geostrophic turbulence Cummins, Patrick F. Journal of Marine Research, Vol. 50, Issue 4 https://doi.org/10.1357/002224092784797548	journal	November 1992
Extreme learning machine: Theory and applications Huang, Guang-Bin; Zhu, Qin-Yu; Siew, Chee-Kheong Neurocomputing, Vol. 70, Issue 1-3 https://doi.org/10.1016/j.neucom.2005.12.126	journal	December 2006
The origins of computer weather prediction and climate modeling Lynch, Peter Journal of Computational Physics, Vol. 227, Issue 7 https://doi.org/10.1016/j.jcp.2007.02.034	journal	March 2008
The Role of Mesoscale Eddies in the General Circulation of the Ocean—Numerical Experiments Using a Wind-Driven Quasi-Geostrophic Model Holland, William R. Journal of Physical Oceanography, Vol. 8, Issue 3 https://doi.org/10.1175/1520-0485(1978)008<0363:TROMEI>2.0.CO;2	journal	May 1978
Increasing horizontal resolution in numerical weather prediction and climate simulations: illusion or panacea? Wedi, Nils P. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2018 https://doi.org/10.1098/rsta.2013.0289	journal	June 2014
Variational Data Assimilation with an Adiabatic Version of the NMC Spectral Model Navon, I. M.; Zou, X.; Derber, J. Monthly Weather Review, Vol. 120, Issue 7 https://doi.org/10.1175/1520-0493(1992)120<1433:VDAWAA>2.0.CO;2	journal	July 1992
Numerical Integration of the Barotropic Vorticity Equation Charney, J. G.; FjÖRtoft, R.; Neumann, J. Tellus, Vol. 2, Issue 4 https://doi.org/10.1111/j.2153-3490.1950.tb00336.x	journal	November 1950
A Proper Orthogonal Decomposition Method for Nonlinear Flows with Deforming Meshes Freno, Brian; Cizmas, Paul 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2013-55	conference	January 2013
On the Wind-Driven Ocean Circulation Morgan, G. W. Tellus, Vol. 8, Issue 3 https://doi.org/10.3402/tellusa.v8i3.9021	journal	January 1956
On the Wind-Driven Ocean Circulation Morgan, G. W. Tellus, Vol. 8, Issue 3 https://doi.org/10.1111/j.2153-3490.1956.tb01228.x	journal	August 1956
Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion: Two-Dimensional Incompressible Flow. Part I Arakawa, Akio Journal of Computational Physics, Vol. 135, Issue 2 https://doi.org/10.1006/jcph.1997.5697	journal	August 1997
Data-assisted reduced-order modeling of extreme events in complex dynamical systems Wan, Zhong Y.; Vlachas, Pantelis; Koumoutsakos, Petros ETH Zurich https://doi.org/10.3929/ethz-b-000268534	text	January 2018
Mesoscale atmosphere ocean coupling enhances the transfer of wind energy into the ocean Byrne, David; Münnich, Matthias; Frenger, Ivy ETH Zurich https://doi.org/10.3929/ethz-b-000117738	text	January 2016
Climate dynamics and fluid mechanics: Natural variability and related uncertainties Ghil, Michael; Chekroun, Mickaël D.; Simonnet, Eric arXiv https://doi.org/10.48550/arxiv.1006.2864	text	January 2010
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
Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison Wang, Zhu; Akhtar, Imran; Borggaard, Jeff arXiv https://doi.org/10.48550/arxiv.1106.3585	text	January 2011
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body Östh, Jan; Noack, Bernd R.; Krajnović, Siniša arXiv https://doi.org/10.48550/arxiv.1310.6285	text	January 2013
An analysis of numerical issues in neural training by pseudoinversion Cancelliere, R.; Deluca, R.; Gai, M. arXiv https://doi.org/10.48550/arxiv.1508.06092	preprint	January 2015
Numerical assessments of ocean energy extraction from western boundary currents using a quasi-geostrophic ocean circulation model San, Omer arXiv https://doi.org/10.48550/arxiv.1604.08486	text	January 2016
Modal Analysis of Fluid Flows: An Overview Taira, Kunihiko; Brunton, Steven L.; Dawson, Scott T. M. arXiv https://doi.org/10.48550/arxiv.1702.01453	preprint	January 2017
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
Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework Wu, Jin-Long; Xiao, Heng; Paterson, Eric arXiv https://doi.org/10.48550/arxiv.1801.02762	text	January 2018
Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model Pathak, Jaideep; Wikner, Alexander; Fussell, Rebeckah arXiv https://doi.org/10.48550/arxiv.1803.04779	text	January 2018

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Title: A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

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