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We propose a new model reduction framework for problems that exhibit transport phenomena.
Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
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A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
Y. Maday, A. T. Patera, and G. Turinici · 2002
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Reduction and reconstruction for self-similar dynamical systems
C. W. Rowley, I. G. Kevrekidis, J. E. Marsden, and K. Lust · 2003
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An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera · 2004
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Freezing solutions of equivariant evolution equations
W. J. Beyn and V. Thümmler · 2004
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Approximation of Large-Scale Dynamical Systems
A. C. Antoulas · 2005
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Reduced-basis approximations and a posteriori error estimation for parabolic partial differential equations
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Theoretical background: Aeroacoustics
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Reduced basis method for finite volume approximations of parametrized linear evolution equations
B. Haasdonk and M. Ohlberger · 2008
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Nonlinear model reduction via discrete empirical interpolation
S. Chaturantabut and D. Sorensen · 2010
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
H. Brezis · 2011
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Model reduction of parametrized evolution problems using the reduced basis method with adaptive time partitioning
M. Dihlmann, M. Drohmann, and B. Haasdonk · 2011
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QLMOR: A projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems
C. Gu · 2011
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Angular synchronization by eigenvectors and semidefinite programming
A. Singer · 2011
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Turbulence, Coherent Structures, Dynamical Systems and Symmetry
P. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley · 2012
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Convergence rates of the POD—greedy method
B. Haasdonk · 2013
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Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
Chapter 1: Proper orthogonal decomposition for linear-quadratic optimal control
M. Gubisch and S. Volkwein · 2017
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A deep learning framework for model reduction of dynamical systems
D. Hartman and L. K. Mestha · 2017
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Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows
R. Mojgani and M. Balajewicz · 2017
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Balanced truncation for linear switched systems
I. V. Gosea, M. Petreczky, A. C. Antoulas, and C. Fiter · 2018
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Model order reduction for stochastic dynamical systems with continuous symmetries
S. Mowlavi and T. P. Sapsis · 2018
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Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling
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A. Janon, M. Nodet, and C. Prieur · 2013
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Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
M. Ohlberger and S. Rave · 2013
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Noisy dynamic simulations in the presence of symmetry: Data alignment and model reduction
B. Sonday, A. Singer, and I. G. Kevrekidis · 2013
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Impact of Discretization Techniques on Nonlinear Model Reduction and Analysis of the Structure of the POD Basis
B. Unger · 2013
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Model order reduction for linear and nonlinear systems: A system-theoretic perspective
U. Baur, P. Benner, and L. Feng · 2014
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Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
J.-F. Gerbeau and D. Lombardi · 2014
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Advection modes by optimal mass transfer
A. Iollo and D. Lombardi · 2014
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B. Peherstorfer · 2018
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ℋ 2 \mathcal{H}_{2} -optimal model approximation by input/output-delay structured reduced order models
I. Pontes Duff, C. Poussot-Vassal, and C. Seren · 2018
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Model reduction for convective problems: formulation and application
J. Reiss · 2018
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The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena
J. Reiss, P. Schulze, J. Sesterhenn, and V. Mehrmann · 2018
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Transport reversal for model reduction of hyperbolic partial differential equations
D. Rim, S. Moe, and R. J. LeVeque · 2018
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Model reduction for linear systems with low-rank switching
P. Schulze and B. Unger · 2018
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Data-driven structured realization
P. Schulze, B. Unger, C. Beattie, and S. Gugercin · 2018
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Model Order Reduction for Problems with Large Convection Effects
N. Cagniart, Y. Maday, and B. Stamm · 2019
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A characteristic dynamic mode decomposition
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A registration method for model order reduction: data compression and geometry reduction
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Kolmogorov n n -widths for linear dynamical systems
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Manifold approximations via transported subspaces: model reduction for transport-dominated problems
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