Balanced Model Reduction via the Proper Orthogonal Decomposition

By Karen E. Willcox, Jaime Peraire. 2002

1,122 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eb44197b41d3adc1c4f831b9870ee5f137ae4956

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Citations in the corpus

Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations (2002, methodology): “The optimality property and generality of these ideas, has led to the successful application of the method in many areas: turbulent flows [60], fluid structure-interaction [22], non-linear structural mechanics [51], turbo-machinery flows [115].”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, methodology): “Many model-order reduction techniques for time-dependent systems are proposed in the literature: the most well-known are proper orthogonal decomposition (POD or Karhunen-Loève decomposition) [40], balanced truncation [26], and various related hybrid [19,45] techniques; see also [20,33] for an applic”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, methodology): “(We note that the greedy sampling methods described in this book are similar in objective to, but very different in approach from, more well-known Proper Orthogonal Decomposition (POD) methods [8, 23, 58, 75, 77, 97, 126, 127, 128, 142, 143, 156] typically applied in the temporal domain.”
Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment (2014, methodology): “Examples of projection-based model reduction approaches include proper orthogonal decomposition (POD) [13, 14, 9], balance d proper orthogonal decomposition (BPOD) [19, 11], balanced truncation [16, 5], the reduced ba sis method [15, 32], and Krylovbased techniques [31].”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, methodology): “There are many approaches to this problem, including discrete empirical interpolation methods (DEIM) [60, 210], gappy POD [100], balanced proper orthogonal decomposition (BPOD) [276, 230], and many more.”
Input–output analysis, model reduction and control of the flat-plate boundary layer (2009, methodology): “snapshot-based balanced truncation ( Willcox & Peraire 2002; Rowley 2005).”
Constrained sparse Galerkin regression (2016, methodology): “Control-theoretic extensions, such as balanced POD (BPOD) (Willcox & Peraire 2002; Rowley 2005), have also been widely applied for closed-loop flow control (Ilak & Rowley 2008; Bagheri, Brandt & Henningson 2009; Illingworth, Morgans & Rowley 2010).”
Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers (2016, methodology): “This methodology has recently been used in investigations of complex flows to either provide an explanation of the essential behavior of the system, or to generate reduced-order models based on a few dominant modes that optimally capture the full dynamics [4,9,17,19, 20].”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “This formulation of Z is very similar to the one computed by the POD method as introduced in [196]: where ( j ω i I − A ) − 1 B , i = 1 , 2 , . . . , m , are called the snap-shots.”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, neutral): “[221] K.”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “(82) Model reduction techniques based on the Proper Orthogonal Decomposition (POD) [131] may be used for constructing a reduced approximation space VM .”
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples (2012, methodology): “The reduced basis [20, 21, 23, 24, 27] and the proper orthogonal decomposition (POD) [12,15, 17, 19, 28] are two techniques belonging to this second family.”