A New Look at Proper Orthogonal Decomposition

By Muruhan Rathinam, Linda R. Petzold. SIAM Journal on Numerical Analysis, 2003

479 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/aee7dff70ab1ae95ec4f40586117a1b0f6d6b5e7

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In Computational Mechanics

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In Statistical and Nonlinear Physics

Citations in the corpus

Nonlinear model order reduction based on local reduced‐order bases (2012, background): “For this reason, many nonlinear MOR methods are equipped with a hyper reduction technique that eliminates this caveat at the cost of an additional approximation [19].”
Constraint reduction procedures for reduced‐order subsurface flow models based on POD–TPWL (2015, background): “Rathinam and Petzold [38], for example, presented an error analysis for POD-based reduced-order ordinary differential equation (ODE) systems.”
Data-driven operator inference for nonintrusive projection-based model reduction (2016, background): “Proper orthogonal decomposition (POD) constructs a reduced basis from states of the full model [1, 2, 7].”
Efficient non‐linear proper orthogonal decomposition/Galerkin reduced order models with stable penalty enforcement of boundary conditions (2012, background): “It is a well-known result [4, 12, 16, 24] that the solution to this optimization problem reduces to the eigenvalue problem R D , where R huk ̋ uki is a self-adjoint and positive semi-definite operator.”
A low‐cost, goal‐oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems (2011, background): “Here, G( , N ) is the set of -dimensional linear subspaces of RN known as the Grassman manifold [9, 25].”
A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation (2008, background): “If the full model dynamics is described by the time-continuous differential system x (t) M(x, t), where x (t) denotes the time derivative, the approximation x̂(t) x (t) to x(t) evolves in time according to the differential equations system (Antoulas 2005; Rathinam and Petzold 2003)”
Using adaptive proper orthogonal decomposition to solve the reaction--diffusion equation (2007, background): “Theoretical considerations, including applications to nonlinear problems, are discussed in [ 32 ].”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “See [194] for a detailed analysis of the error of a POD-based reduced model.”
A method to construct reduced‐order parameter‐varying models (2017, background): “Despite the connection of POD/Galerkin to controls, there have been many studies done that show that POD/Galerkin is sensitive inputs and to the data used [37] Also, it can often produce unstable results near stable equilibrium [38].”
A projection method for model reduction of bilinear dynamical systems (2006, background): “The interested reader is referred to [10,23,12,13] and references therein.”
An Online Method for Interpolating Linear Parametric Reduced-Order Models (2011, background): “Define a trial basis V(μ) ∈ Rn×k having full-column rank and describing a trial subspace SV(μ) belonging to the Grassmann manifold G(k, n) [3, 10].”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “In [70], the error bounds of solutions from a POD reduced system were derived and the effects of small perturbations on the set of snapshots used for constructing the POD basis were studied.”