Model reduction for nonlinear dynamical systems using deep convolutional autoencoders.

Lee, Kookjin; Carlberg, Kevin Thomas

doi:10.1016/j.jcp.2019.108973

Model reduction for nonlinear dynamical systems using deep convolutional autoencoders.

Conference · Sat Dec 01 04:00:00 UTC 2018

DOI:https://doi.org/10.1016/j.jcp.2019.108973· OSTI ID:1761319

Lee, Kookjin; Carlberg, Kevin Thomas

Abstract not provided.

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Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

DOE Contract Number:: AC04-94AL85000

OSTI ID:: 1761319

Report Number(s):: SAND2018-13766C; 670887

Country of Publication:: United States

Language:: English

References (44)

Principal component analysis in linear systems: Controllability, observability, and model reduction Moore, B. IEEE Transactions on Automatic Control, Vol. 26, Issue 1 https://doi.org/10.1109/TAC.1981.1102568	journal	February 1981
Adaptive h -refinement for reduced-order models : ADAPTIVE Carlberg, Kevin International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5 https://doi.org/10.1002/nme.4800	journal	November 2014
Conservative model reduction for finite-volume models Carlberg, Kevin; Choi, Youngsoo; Sargsyan, Syuzanna Journal of Computational Physics, Vol. 371 https://doi.org/10.1016/j.jcp.2018.05.019	journal	October 2018
Learning representations by back-propagating errors Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. Nature, Vol. 323, Issue 6088 https://doi.org/10.1038/323533a0	journal	October 1986
Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel International Journal for Numerical Methods in Engineering, Vol. 86, Issue 2 https://doi.org/10.1002/nme.3050	journal	October 2010
Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart Computer Methods in Applied Mechanics and Engineering, Vol. 289 https://doi.org/10.1016/j.cma.2015.02.013	journal	June 2015
A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems Carlberg, Kevin; Farhat, Charbel International Journal for Numerical Methods in Engineering, Vol. 86, Issue 3 https://doi.org/10.1002/nme.3074	journal	December 2010
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations Rozza, G.; Huynh, D. B. P.; Patera, A. T. Archives of Computational Methods in Engineering, Vol. 15, Issue 3 https://doi.org/10.1007/BF03024948	journal	September 2007
Reducing the Dimensionality of Data with Neural Networks Hinton, G. E. Science, Vol. 313, Issue 5786 https://doi.org/10.1126/science.1127647	journal	July 2006
Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods Prud’homme, C.; Rovas, D. V.; Veroy, K. Journal of Fluids Engineering, Vol. 124, Issue 1 https://doi.org/10.1115/1.1448332	journal	November 2001
Convergence Rates for Greedy Algorithms in Reduced Basis Methods Binev, Peter; Cohen, Albert; Dahmen, Wolfgang SIAM Journal on Mathematical Analysis, Vol. 43, Issue 3 https://doi.org/10.1137/100795772	journal	January 2011
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation Belkin, Mikhail; Niyogi, Partha Neural Computation, Vol. 15, Issue 6 https://doi.org/10.1162/089976603321780317	journal	June 2003
Practical quasi-Newton methods for solving nonlinear systems Martı́nez, José Mario Journal of Computational and Applied Mathematics, Vol. 124, Issue 1-2 https://doi.org/10.1016/S0377-0427(00)00434-9	journal	December 2000
Balanced Model Reduction via the Proper Orthogonal Decomposition Willcox, K.; Peraire, J. AIAA Journal, Vol. 40, Issue 11 https://doi.org/10.2514/2.1570	journal	November 2002
Deep learning for universal linear embeddings of nonlinear dynamics Lusch, Bethany; Kutz, J. Nathan; Brunton, Steven L. arXiv https://doi.org/10.48550/arxiv.1712.09707	text	January 2017
Progressive construction of a parametric reduced-order model for PDE-constrained optimization: PDE-CONSTRAINED OPTIMIZATION USING A PROGRESSIVELY CONSTRUCTED ROM Zahr, Matthew J.; Farhat, Charbel International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5 https://doi.org/10.1002/nme.4770	journal	December 2014
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows Carlberg, Kevin; Farhat, Charbel; Cortial, Julien Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.02.028	journal	June 2013
A subspace approach to balanced truncation for model reduction of nonlinear control systems Lall, Sanjay; Marsden, Jerrold E.; Glava?ki, Sonja International Journal of Robust and Nonlinear Control, Vol. 12, Issue 6 https://doi.org/10.1002/rnc.657	journal	January 2002
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems Gugercin, S.; Antoulas, A. C.; Beattie, C. SIAM Journal on Matrix Analysis and Applications, Vol. 30, Issue 2 https://doi.org/10.1137/060666123	journal	January 2008
Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification Crisovan, R.; Torlo, D.; Abgrall, R. Journal of Computational and Applied Mathematics, Vol. 348 https://doi.org/10.1016/j.cam.2018.09.018	journal	March 2019
Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction Carlberg, Kevin; Barone, Matthew; Antil, Harbir Journal of Computational Physics, Vol. 330 https://doi.org/10.1016/j.jcp.2016.10.033	journal	February 2017
Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing Ohlberger, Mario; Rave, Stephan Comptes Rendus Mathematique, Vol. 351, Issue 23-24 https://doi.org/10.1016/j.crma.2013.10.028	journal	December 2013
Analysis of a complex of statistical variables into principal components. Hotelling, H. Journal of Educational Psychology, Vol. 24, Issue 6 https://doi.org/10.1037/h0071325	journal	January 1933
Model Reduction for Fluids, Using Balanced Proper Orthogonal Decomposition Rowley, C. W. International Journal of Bifurcation and Chaos, Vol. 15, Issue 03 https://doi.org/10.1142/S0218127405012429	journal	March 2005
Optimization Methods for Large-Scale Machine Learning Bottou, Léon; Curtis, Frank E.; Nocedal, Jorge SIAM Review, Vol. 60, Issue 2 https://doi.org/10.1137/16M1080173	journal	January 2018
Advection modes by optimal mass transfer Iollo, Angelo; Lombardi, Damiano Physical Review E, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevE.89.022923	journal	February 2014
Deep learning LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey Nature, Vol. 521, Issue 7553 https://doi.org/10.1038/nature14539	journal	May 2015
Interpolatory Projection Methods for Parameterized Model Reduction Baur, Ulrike; Beattie, Christopher; Benner, Peter SIAM Journal on Scientific Computing, Vol. 33, Issue 5 https://doi.org/10.1137/090776925	journal	January 2011
Coupling of substructures for dynamic analyses. Craig, Roy R.; Bampton, Mervyn C. C. AIAA Journal, Vol. 6, Issue 7 https://doi.org/10.2514/3.4741	journal	July 1968
Nonlinear Dimensionality Reduction by Locally Linear Embedding Roweis, S. T. Science, Vol. 290, Issue 5500 https://doi.org/10.1126/science.290.5500.2323	journal	December 2000
Nonlinear Component Analysis as a Kernel Eigenvalue Problem Schölkopf, Bernhard; Smola, Alexander; Müller, Klaus-Robert Neural Computation, Vol. 10, Issue 5 https://doi.org/10.1162/089976698300017467	journal	July 1998
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs Bachmayr, Markus; Cohen, Albert Mathematics of Computation, Vol. 86, Issue 304 https://doi.org/10.1090/mcom/3132	journal	July 2016
Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data Donoho, D. L.; Grimes, C. Proceedings of the National Academy of Sciences, Vol. 100, Issue 10 https://doi.org/10.1073/pnas.1031596100	journal	April 2003
Gradient-based learning applied to document recognition Lecun, Y.; Bottou, L.; Bengio, Y. Proceedings of the IEEE, Vol. 86, Issue 11 https://doi.org/10.1109/5.726791	journal	January 1998
Model reduction using L ¹ -norm minimization as an application to nonlinear hyperbolic problems: Model reduction for hyperbolic problems Abgrall, R.; Crisovan, R. International Journal for Numerical Methods in Fluids, Vol. 87, Issue 12 https://doi.org/10.1002/fld.4507	journal	April 2018
Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates Peherstorfer, Benjamin; Willcox, Karen SIAM Journal on Scientific Computing, Vol. 37, Issue 4 https://doi.org/10.1137/140989169	journal	January 2015
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
Interpolation of Functions with Parameter Dependent Jumps by Transformed Snapshots Welper, G. SIAM Journal on Scientific Computing, Vol. 39, Issue 4 https://doi.org/10.1137/16M1059904	journal	January 2017
The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena Reiss, J.; Schulze, P.; Sesterhenn, J. SIAM Journal on Scientific Computing, Vol. 40, Issue 3 https://doi.org/10.1137/17M1140571	journal	January 2018
Self-organized formation of topologically correct feature maps Kohonen, Teuvo Biological Cybernetics, Vol. 43, Issue 1 https://doi.org/10.1007/BF00337288	journal	January 1982
Reduced basis techniques for nonlinear conservation laws Taddei, T.; Perotto, S.; Quarteroni, A. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 49, Issue 3 https://doi.org/10.1051/m2an/2014054	journal	April 2015
A Global Geometric Framework for Nonlinear Dimensionality Reduction Tenenbaum, J. B. Science, Vol. 290, Issue 5500 https://doi.org/10.1126/science.290.5500.2319	journal	December 2000
Nonlinear model order reduction based on local reduced-order bases: NONLINEAR MODEL REDUCTION BASED ON LOCAL REDUCED-ORDER BASES Amsallem, David; Zahr, Matthew J.; Farhat, Charbel International Journal for Numerical Methods in Engineering, Vol. 92, Issue 10 https://doi.org/10.1002/nme.4371	journal	June 2012
Approximated Lax pairs for the reduced order integration of nonlinear evolution equations Gerbeau, Jean-Frédéric; Lombardi, Damiano Journal of Computational Physics, Vol. 265 https://doi.org/10.1016/j.jcp.2014.01.047	journal	May 2014

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