Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition

By Clarence W. Rowley. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2005

1,023 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4f62cf2e99315e5585ad4c77e76aa6b4b80cf338

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

A method to construct reduced‐order parameter‐varying models (2017, methodology): “POD modes have been used to construct reduced-order models that can be used for control such as balanced POD [19, 20].”
Optimal mode decomposition for unsteady flows (2013, background): “An alternative extension of POD was proposed by Rowley (2005) in the context of snapshot data sampled from a controlled system.”
Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems (2007, neutral): “The relationship between POD and balancing was considered in [15] [20] [23].”
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators (2009, methodology): “Since the models obtained using balanced truncation are known to perform better than the POD– Galerkin models, as reported by Ilak & Rowley (2008), the better performance could be attributed to a better choice of projection using the adjoint modes.”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, methodology): “For this section, we consider the eigensystem realization algorithm (ERA) and observer-Kalman filter identification (OKID) methods because of their connection to balanced model reduction [192, 230, 181, 269] and their recent successful application in closed-loop flow control [13, 11, 143].”
Model Reduction for Flow Analysis and Control (2017, methodology): “(17) The method discussed above was originally presented by Rowley (2005), and the idea of empirical Gramians was provided by Lall et al. (1999, 2002).”
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks (2018, background): “A major beneficiary of this convergence are data-driven dimensionality reduction methods [7, 2, 3, 5, 6, 4, 8], model identification procedures [11, 10, 12, 13, 14, 15, 16, 9] and forecasting techniques [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] that aim to provide precise short-te”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “POD has been successfully used with a Galerkin projection to provide reduced-order models in numerous applications such as compressible flow [78], computational fluid dynamics [50, 77], aerodynamics [14], and optimal control [48].”
Generalizing Koopman Theory to Allow for Inputs and Control (2016, neutral): “On these lowdimensional subspaces, controllers can be described, constructed, and implemented [35, 23, 19, 41, 40, 39, 53, 17].”
Dynamic Mode Decomposition with Control (2014, methodology): “trollers can be designed and implemented [29], [20], [17], [31].”
Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach (2010, methodology): “Moreover, Rowley [100] noted that the eigenvectors of the controllability Gramian (instead of the product of the Gramians) yield a POD-type basis.”
Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction (2011, background): “Furthermore, the balanced POD serves as economic expansion for linear input–output relationships (Rowley 2005).”
A low‐cost, goal‐oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems (2011, neutral): “This approach bears similarities to Balanced POD [31], as (·, ·)H (̄)T H (̄) can be interpreted as an observability inner product.”
Sparsity-promoting dynamic mode decomposition (2012, background): “For example, proper orthogonal decomposition (POD) modes [1, 2], global eigenmodes, frequential modes [3], and balanced modes [4, 5] have provided useful insight into the dynamics of fluid flows.”
Enablers for robust POD models (2009, methodology): “Key words: Proper Orthogonal Decomposition, Reduced Order Model, Stabilization, Functional subspace improvement”