Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Journal of Computational Physics ◽

10.1016/j.jcp.2019.108973 ◽

2020 ◽

Vol 404 ◽

pp. 108973 ◽

Author(s):

Kookjin Lee ◽

Kevin T. Carlberg

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Nonlinear Manifolds

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A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-021-01521-0 ◽

2021 ◽

Author(s):

M. A. Hamadi ◽

K. Jbilou ◽

A. Ratnani

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Large Scale ◽

Reduction Method ◽

Arnoldi Method ◽

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Preserving general physical properties in model reduction of dynamical systems via constrained‐optimization projection

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6667 ◽

2021 ◽

Author(s):

Alexander Schein ◽

Kevin T. Carlberg ◽

Matthew J. Zahr

Keyword(s):

Dynamical Systems ◽

Physical Properties ◽

Constrained Optimization ◽

Model Reduction ◽

General Physical

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Model Reduction with Memory and the Machine Learning of Dynamical Systems

Communications in Computational Physics ◽

10.4208/cicp.oa-2018-0269 ◽

2019 ◽

Vol 25 (4) ◽

Author(s):

Chao Ma ◽

Jianchun Wang ◽

Weinan E

Keyword(s):

Machine Learning ◽

Dynamical Systems ◽

Model Reduction ◽

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Benchmark Examples for Model Reduction of Linear Time-Invariant Dynamical Systems

Lecture Notes in Computational Science and Engineering - Dimension Reduction of Large-Scale Systems ◽

10.1007/3-540-27909-1_24 ◽

2005 ◽

pp. 379-392 ◽

Author(s):

Younes Chahlaoui ◽

Paul Van Dooren

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Linear Time ◽

Linear Time Invariant ◽

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Model Reduction of Complex Dynamical Systems

10.1007/978-3-030-72983-7 ◽

2021 ◽

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Complex Dynamical Systems

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Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ1-regularization

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5139463 ◽

2020 ◽

Vol 30 (5) ◽

pp. 053122

Author(s):

Q. Yang ◽

C. A. Sing-Long ◽

E. J. Reed

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Chemical Reaction ◽

Nonlinear Dynamical Systems ◽

Chemical Reaction Networks ◽

Data Driven ◽

Reaction Networks ◽

Nonlinear Dynamical ◽

ℓ1 Regularization

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A model-reduction method for nonlinear discrete-time skew-product dynamical systems in the presence of model uncertainty

Nonlinear Dynamics ◽

10.1007/s11071-010-9738-y ◽

2010 ◽

Vol 62 (3) ◽

pp. 521-534 ◽

Author(s):

Nikolaos Kazantzis

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Discrete Time ◽

Model Uncertainty ◽

Reduction Method ◽

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A Tangential Block Lanczos Method for Model Reduction of Large-Scale First and Second Order Dynamical Systems

Journal of Scientific Computing ◽

10.1007/s10915-019-01032-y ◽

2019 ◽

Vol 81 (1) ◽

pp. 513-536

Author(s):

K. Jbilou ◽

Y. Kaouane

Keyword(s):

Dynamical Systems ◽

Model Reduction ◽

Large Scale ◽

Lanczos Method ◽

Second Order ◽

Block Lanczos ◽

Block Lanczos Method

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Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2020.132614 ◽

2020 ◽

Vol 412 ◽

pp. 132614

Author(s):

Han Gao ◽

Jian-Xun Wang ◽

Matthew J. Zahr

Keyword(s):

Deep Learning ◽

Dynamical Systems ◽

Model Reduction ◽

Large Scale ◽

Nonlinear Dynamical Systems ◽

Nonlinear Dynamical

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Model reduction for large-scale dynamical systems via equality constrained least squares

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2010.03.006 ◽

2010 ◽

Vol 234 (8) ◽

pp. 2420-2431 ◽

Author(s):

Yu’e An ◽

Chuanqing Gu

Keyword(s):

Dynamical Systems ◽

Least Squares ◽

Model Reduction ◽

Large Scale ◽

Constrained Least Squares ◽

Equality Constrained Least Squares

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