PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY

By Yanchun Liang, H. P. Lee, S. Lim, W. Z. Lin, K. H. Lee, C. G. Wu. 2002

805 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/37500aa3a0ceb7a8c25b545e449a5a14d5fb8afc

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Citations in the corpus

A New Data-Space Inversion Procedure for Efficient Uncertainty Quantification in Subsurface Flow Problems (2017, methodology): “See Shlens (2005) for a tutorial on PCA and Liang et al. (2002) for theory and proofs. The application of PCA to reparameterize reservoir model parameters has been discussed by many authors; see, e.g., Oliver (1996), Reynolds et al.”
Non-intrusive reduced order modeling of nonlinear problems using neural networks (2018, methodology): “For this, two major approaches have been proposed in the literature: proper orthogonal decomposition (POD) [22, 46] and greedy algorithms [24].”
The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains (2007, methodology): “[31]) that the error induced by the K–L procedure is given by:”
Numerical Modelling of Natural Draft Wet-Cooling Towers (2013, methodology): “The PCA can be equivalently seen as either a variance maximization technique or a least-mean-squares technique [53].”
Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables (2015, methodology): “POD is a method to obtain a low-dimensional approximation to a high-dimensional space by the derivation of dominant components, or modes, and can be done by principal component analysis, Karhunen–Loeve decomposition, or singular value decomposition [43], though these methods can be shown to be equiv”
Data-driven reduced order modeling for time-dependent problems (2019, methodology): “the Greedy algorithm [32, 38, 43] and the proper orthogonal decomposition (POD) [18, 23, 36].”
Development and evaluation of gappy-POD as a data reconstruction technique for noisy PIV measurements in gas turbine combustors (2016, methodology): “The main feature of POD is that it provides the most efficient way of capturing dominant components in the data by constructing the approximation using only the most energetic modes (Liang et al, 2002).”
Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis (2005, methodology): “It can be shown [6] that the constraint optimum problem posed by (9) and (10) is equivalent to the following eigenvalue problem: Cvi = ivi (11)”
A deep learning-based hybrid approach for the solution of multiphysics problems in electrosurgery (2019, methodology): “POD is a general technique for extracting the most significant features of a system’s behavior and representing them using a set of POD bases spanning the reduced-order subspace [13,14].”
The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview (2005, methodology): “The reader is referred to references [11–15] for a detailed discussion about the equivalence of the POD, PCA and KLD, and their connection with the singular value decomposition (SVD).”
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, background): “For an overview of proper orthogonal decomposition, see [37,34].”
POD‐based model reduction with empirical interpolation applied to nonlinear elasticity (2016, methodology): “It is also known as Karhunen-Loéve decomposition, principal component analysis, or singular value decomposition [4, 5].”
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis (2017, background): “Some articles describe POD in purely abstract terms and make no distinction between the two versions of the method (Berkooz et al., 1993; Liang et al., 2002).”