Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition

By Tan Bui-Thanh, M. Damodaran, Karen E. Willcox. 2004

542 citations recorded by the source corpus.

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

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Citations in the corpus

Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow (2018, neutral): “An important difference is also that these methods, similar to other model reduction techniques [27], and POD-based methods [5] have so far has only been demonstrated for single-phase simulations.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “Interpolation can be achieved using polynomial or spline interpolation [60, 163, 69], least squares fitting [59, 178], or radial basis function models [20].”
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems (2019, methodology): “, via gappy POD [5, 6], or using radial basis functions [7], a neural network [8, 9, 10] or a nearest-neighbors method [10].”
Surrogate Modeling Approach to Support Real-Time Structural Assessment and Decision Making (2015, methodology): “We use the gappy POD method [53,54] to rapidly reconstruct the measurement POD coefficients αj given the sensor measurement data q̂m.”
Using adaptive proper orthogonal decomposition to solve the reaction--diffusion equation (2007, methodology): “Proper orthogonal decomposition is used in many disciplines of science and engineering, including fluid mechanics [16,47], data reconstruction [ 5 ,49], controls [1,25,33], heat transfer [30,31], nondestructive evaluation [17], and biology [26].”
Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization (2010, background): “As shown throughout the literature [10,11], POD cannot accurately represent data outside of the initial snapshot ensemble.”
Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition (2004, methodology): “The gappy POD has also been applied for reconstruction of airfoil pressure fields from limited surface measurements [14].”
Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media (2011, background): “Numerical results demonstrate that the dynamics of the viscous fingering in the full-order system of dimension 15,000 can be captured accurately by the POD–DEIM reduced system of dimension 40 with the computational time reduced by factor of O(1000).”
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition (2008, unknown): “The gappy POD method has been applied to data reconstruction problems, such as reconstruction of facial images [17], flow structure [12], [42], and flow sensing [44].”
Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations (2011, methodology): “It has also been used for steady [41, 42] and unsteady [43, 44] ﬂow ﬁeld reconstruction, inverse design [42], design variable mapping for multi-ﬁdelity optimization [45], and to some extent, for non-linear computations [26, 46].”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “63,216,217 Examples of hyperreduction include the empirical interpolation method (EIM), 86 its discrete version (DEIM), 90,218 the gappy POD, 100,111,219 and the missing point estimation (MPE), 108,220 where the approximation is performed using sampling techniques.”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “The POD-Galerkin approach has provided reduced-order models of systems in numerous applications such as compressible flow [38], fluid dynamics [23], aerodynamics [9], and optimal control [22].”
Projection-based model reduction: Formulations for physics-based machine learning (2019, methodology): “in [13] reconstructs POD representations of aerodynamic quantities from incomplete data using interpolation via the gappy POD [14].”