Numerical Assessment of a Nonintrusive Surrogate Model Based on Recurrent Neural Networks and Proper Orthogonal Decomposition: Rayleigh–Bénard Convection

Akbari, Saeed; Pawar, Suraj; San, Omer

doi:10.1080/10618562.2022.2154918

Numerical Assessment of a Nonintrusive Surrogate Model Based on Recurrent Neural Networks and Proper Orthogonal Decomposition: Rayleigh–Bénard Convection

Journal Article · 09 August 2022 · International Journal of Computational Fluid Dynamics

DOI:https://doi.org/10.1080/10618562.2022.2154918· OSTI ID:1979230

^[1]; Pawar, Suraj ^[1]; ^[1]

Oklahoma State University Stillwater, Stillwater, OK, USA

Not provided.

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

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0019290

OSTI ID:: 1979230

Journal Information:: International Journal of Computational Fluid Dynamics, Vol. 36, Issue 7; ISSN 1061-8562

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

References (54)

A predictive hybrid reduced order model based on proper orthogonal decomposition combined with deep learning architectures Abadía-Heredia, R.; López-Martín, M.; Carro, B. Expert Systems with Applications, Vol. 187 https://doi.org/10.1016/j.eswa.2021.115910	journal	January 2022
Stabilized principal interval decomposition method for model reduction of nonlinear convective systems with moving shocks Ahmed, Mansoor; San, Omer Computational and Applied Mathematics, Vol. 37, Issue 5 https://doi.org/10.1007/s40314-018-0718-z	journal	September 2018
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues Ahmed, Shady E.; Pawar, Suraj; San, Omer Physics of Fluids, Vol. 33, Issue 9 https://doi.org/10.1063/5.0061577	journal	September 2021
Breaking the Kolmogorov Barrier in Model Reduction of Fluid Flows Ahmed, Shady E.; San, Omer Fluids, Vol. 5, Issue 1 https://doi.org/10.3390/fluids5010026	journal	February 2020
A long short-term memory embedding for hybrid uplifted reduced order models Ahmed, Shady E.; San, Omer; Rasheed, Adil Physica D: Nonlinear Phenomena, Vol. 409 https://doi.org/10.1016/j.physd.2020.132471	journal	August 2020
Nonlinear proper orthogonal decomposition for convection-dominated flows Ahmed, Shady E.; San, Omer; Rasheed, Adil Physics of Fluids, Vol. 33, Issue 12 https://doi.org/10.1063/5.0074310	journal	December 2021
PEBL-ROM: Projection-error based local reduced-order models Amsallem, David; Haasdonk, Bernard Advanced Modeling and Simulation in Engineering Sciences, Vol. 3, Issue 1 https://doi.org/10.1186/s40323-016-0059-7	journal	March 2016
Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction Amsallem, David; Zahr, Matthew J.; Washabaugh, Kyle Advances in Computational Mathematics, Vol. 41, Issue 5 https://doi.org/10.1007/s10444-015-9409-0	journal	February 2015
Preserving Symmetries in the Proper Orthogonal Decomposition Aubry, Nadine; Lian, Wen-Yu; Titi, Edriss S. SIAM Journal on Scientific Computing, Vol. 14, Issue 2 https://doi.org/10.1137/0914030	journal	March 1993
Enablers for robust POD models Bergmann, M.; Bruneau, C. -H.; Iollo, A. Journal of Computational Physics, Vol. 228, Issue 2 https://doi.org/10.1016/j.jcp.2008.09.024	journal	February 2009
A numerical study of laminar separation bubbles using the Navier-Stokes equations Briley, W. Roger Journal of Fluid Mechanics, Vol. 47, Issue 4 https://doi.org/10.1017/S0022112071001332	journal	June 1971
Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun SIAM Journal on Scientific Computing, Vol. 28, Issue 2 https://doi.org/10.1137/5106482750342221x	journal	January 2006
POD and CVT-based reduced-order modeling of Navier–Stokes flows Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 1-3 https://doi.org/10.1016/j.cma.2006.04.004	journal	December 2006
Acquisition of kHz-frequency two-dimensional surface temperature field using phosphor thermometry and proper orthogonal decomposition assisted long short-term memory neural networks Cai, Tao; Deng, Zhiwen; Park, Yoonseong International Journal of Heat and Mass Transfer, Vol. 165 https://doi.org/10.1016/j.ijheatmasstransfer.2020.120662	journal	February 2021
Evaluation of Proper Orthogonal Decomposition--Based Decomposition Techniques Applied to Parameter-Dependent Nonturbulent Flows Christensen., Erik Adler; Brøns, Morten; Sørensen, Jens Nørkær SIAM Journal on Scientific Computing, Vol. 21, Issue 4 https://doi.org/10.1137/S1064827598333181	journal	January 1999
Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders Deane, A. E.; Kevrekidis, I. G.; Karniadakis, G. E. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 10 https://doi.org/10.1063/1.857881	journal	October 1991
Adaptive Reduced Basis Methods for Nonlinear Convection–Diffusion Equations Drohmann, Martin; Haasdonk, Bernard; Ohlberger, Mario Finite Volumes for Complex Applications VI Problems & Perspectives https://doi.org/10.1007/978-3-642-20671-9_39	book	January 2011
Anhpcertified reduced basis method for parametrized parabolic partial differential equations Eftang, Jens L.; Knezevic, David J.; Patera, Anthony T. Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, Issue 4 https://doi.org/10.1080/13873954.2011.547670	journal	August 2011
An "$hp$" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. SIAM Journal on Scientific Computing, Vol. 32, Issue 6 https://doi.org/10.1137/090780122	journal	January 2010
Parameter multi-domain ‘hp’ empirical interpolation: PARAMETER MULTI-DOMAIN ‘hp’ EMPIRICAL INTERPOLATION Eftang, Jens L.; Stamm, Benjamin International Journal for Numerical Methods in Engineering, Vol. 90, Issue 4 https://doi.org/10.1002/nme.3327	journal	March 2012
Deep neural networks for nonlinear model order reduction of unsteady flows Eivazi, Hamidreza; Veisi, Hadi; Naderi, Mohammad Hossein Physics of Fluids, Vol. 32, Issue 10 https://doi.org/10.1063/5.0020526	journal	October 2020
Simulation of lead-acid battery using model order reduction Esfahanian, Vahid; Ansari, Amir Babak; Torabi, Farschad Journal of Power Sources, Vol. 279 https://doi.org/10.1016/j.jpowsour.2014.12.149	journal	April 2015
Decay of the Kolmogorov N -width for wave problems Greif, Constantin; Urban, Karsten Applied Mathematics Letters, Vol. 96 https://doi.org/10.1016/j.aml.2019.05.013	journal	October 2019
A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space Haasdonk, Bernard; Dihlmann, Markus; Ohlberger, Mario Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, Issue 4 https://doi.org/10.1080/13873954.2011.547674	journal	August 2011
Long Short-Term Memory Hochreiter, Sepp; Schmidhuber, Jürgen Neural Computation, Vol. 9, Issue 8 https://doi.org/10.1162/neco.1997.9.8.1735	journal	November 1997
Turbulence, Coherent Structures, Dynamical Systems and Symmetry Holmes, Philip; Lumley, John L.; Berkooz, Gahl Cambridge University Press https://doi.org/10.1017/CBO9780511919701	book	January 2012
Low-dimensional models of coherent structures in turbulence Holmes, Philip J.; Lumley, John L.; Berkooz, Gal Physics Reports, Vol. 287, Issue 4 https://doi.org/10.1016/S0370-1573(97)00017-3	journal	August 1997
A machine learning based plasticity model using proper orthogonal decomposition Huang, Dengpeng; Fuhg, Jan Niklas; Weißenfels, Christian Computer Methods in Applied Mechanics and Engineering, Vol. 365 https://doi.org/10.1016/j.cma.2020.113008	journal	June 2020
Surrogate modeling of elasto-plastic problems via long short-term memory neural networks and proper orthogonal decomposition Im, Sunyoung; Lee, Jonggeon; Cho, Maenghyo Computer Methods in Applied Mechanics and Engineering, Vol. 385 https://doi.org/10.1016/j.cma.2021.114030	journal	November 2021
Non-intrusive reduced-order modeling using uncertainty-aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to flood modeling Jacquier, Pierre; Abdedou, Azzedine; Delmas, Vincent Journal of Computational Physics, Vol. 424 https://doi.org/10.1016/j.jcp.2020.109854	journal	January 2021
Cluster-based reduced-order modelling of a mixing layer Kaiser, Eurika; Noack, Bernd R.; Cordier, Laurent Journal of Fluid Mechanics, Vol. 754 https://doi.org/10.1017/jfm.2014.355	journal	August 2014
An intrinsic stabilization scheme for proper orthogonal decomposition based low-dimensional models Kalb, Virginia L.; Deane, Anil E. Physics of Fluids, Vol. 19, Issue 5 https://doi.org/10.1063/1.2723149	journal	May 2007
A probabilistic graphical model foundation for enabling predictive digital twins at scale Kapteyn, Michael G.; Pretorius, Jacob V. R.; Willcox, Karen E. Nature Computational Science, Vol. 1, Issue 5 https://doi.org/10.1038/s43588-021-00069-0	journal	May 2021
Uber Die Beste Annaherung Von Funktionen Einer Gegebenen Funktionenklasse Kolmogoroff, A. The Annals of Mathematics, Vol. 37, Issue 1 https://doi.org/10.2307/1968691	journal	January 1936
Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition Kunisch, K.; Volkwein, S. Journal of Optimization Theory and Applications, Vol. 102, Issue 2 https://doi.org/10.1023/A:1021732508059	journal	August 1999
Galerkin proper orthogonal decomposition methods for parabolic problems Kunisch, K.; Volkwein, S. Numerische Mathematik, Vol. 90, Issue 1 https://doi.org/10.1007/s002110100282	journal	November 2001
Compact finite difference schemes with spectral-like resolution Lele, Sanjiva K. Journal of Computational Physics, Vol. 103, Issue 1 https://doi.org/10.1016/0021-9991(92)90324-R	journal	November 1992
Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders Maulik, Romit; Lusch, Bethany; Balaprakash, Prasanna Physics of Fluids, Vol. 33, Issue 3 https://doi.org/10.1063/5.0039986	journal	March 2021
A deep learning enabler for nonintrusive reduced order modeling of fluid flows Pawar, S.; Rahman, S. M.; Vaddireddy, H. Physics of Fluids, Vol. 31, Issue 8 https://doi.org/10.1063/1.5113494	journal	August 2019
LIII. On lines and planes of closest fit to systems of points in space Pearson, Karl The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 2, Issue 11 https://doi.org/10.1080/14786440109462720	journal	November 1901
Localized Discrete Empirical Interpolation Method Peherstorfer, Benjamin; Butnaru, Daniel; Willcox, Karen SIAM Journal on Scientific Computing, Vol. 36, Issue 1 https://doi.org/10.1137/130924408	journal	January 2014
IEEE Access No authors listed https://doi.org/10.1109/Access.6287639	journal
A New Look at Proper Orthogonal Decomposition Rathinam, Muruhan; Petzold, Linda R. SIAM Journal on Numerical Analysis, Vol. 41, Issue 5 https://doi.org/10.1137/S0036142901389049	journal	January 2003
A POD-EIM reduced two-scale model for crystal growth Redeker, Magnus; Haasdonk, Bernard Advances in Computational Mathematics, Vol. 41, Issue 5 https://doi.org/10.1007/s10444-014-9367-y	journal	July 2014
A Novel High-Order Accurate Compact Stencil Poisson Solver: Application to Cavity Flows San, Omer International Journal of Applied Mechanics, Vol. 07, Issue 01 https://doi.org/10.1142/S1758825115400062	journal	February 2015
Neural network closures for nonlinear model order reduction San, Omer; Maulik, Romit Advances in Computational Mathematics, Vol. 44, Issue 6 https://doi.org/10.1007/s10444-018-9590-z	journal	January 2018
An artificial neural network framework for reduced order modeling of transient flows San, Omer; Maulik, Romit; Ahmed, Mansoor Communications in Nonlinear Science and Numerical Simulation, Vol. 77 https://doi.org/10.1016/j.cnsns.2019.04.025	journal	October 2019
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
Predictions of turbulent shear flows using deep neural networks Srinivasan, P. A.; Guastoni, L.; Azizpour, H. Physical Review Fluids, Vol. 4, Issue 5 https://doi.org/10.1103/PhysRevFluids.4.054603	journal	May 2019
The role of artificial intelligence in achieving the Sustainable Development Goals Vinuesa, Ricardo; Azizpour, Hossein; Leite, Iolanda Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-019-14108-y	journal	January 2020
Deep Learning-Based Model Reduction for Distributed Parameter Systems Wang, Mingliang; Li, Han-Xiong; Chen, Xin IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 46, Issue 12 https://doi.org/10.1109/TSMC.2016.2605159	journal	December 2016
Nonlinear Model Reduction for CFD Problems Using Local Reduced-Order Bases Washabaugh, Kyle; Amsallem, David; Zahr, Matthew 42nd AIAA Fluid Dynamics Conference and Exhibit https://doi.org/10.2514/6.2012-2686	conference	September 2012
Essentially Compact Schemes for Unsteady Viscous Incompressible Flows E., Weinan; Liu, Jian-Guo Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0125	journal	June 1996
Implicit partitioning methods for unknown parameter sets Wieland, Bernhard Advances in Computational Mathematics, Vol. 41, Issue 5 https://doi.org/10.1007/s10444-015-9404-5	journal	August 2015

Similar Records

An Investigation of LES Wall Modeling for Rayleigh–Bénard Convection via Interpretable and Physics-Aware Feedforward Neural Networks with DNS

Journal Article · 2024 · Journal of the Atmospheric Sciences · OSTI ID:2301730

Wang, Aaron; Yang, Xiang A.; Ovchinnikov, Mikhail

Related Subjects

Mechanics
Physics

Numerical Assessment of a Nonintrusive Surrogate Model Based on Recurrent Neural Networks and Proper Orthogonal Decomposition: Rayleigh–Bénard Convection

Citation Formats

References (54)

Similar Records

Related Subjects