Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis

By Joris Degroote, Jan A. Vierendeels, Karen E. Willcox. 2009

138 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f52df5d85c384915bf6e70a557845525e3472c9f

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In Numerical Analysis

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Evaluation of aerodynamic loads via reduced order methodology (2015, methodology): “Intrusive methods elaborate on the mathematics of the projection step to reformulate the original system of partial differential equations (PDEs) as a system of ordinary differential equations (ODEs), with the modal coefficients as unknowns [3–6].”
Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media (2017, methodology): “e governing equations is attempted [78,16]. Naturally such an assumption ceases to hold as higher-dimensional inputs are considered and various strategies have been adopted to address this limitation [17,21,45]. The potential of dimensionality-reduction methods in overcoming the curse of dimensional”
A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models (2017, methodology): “This approach was shown to be computationally efficient for both a -parametric HDM and its associated -parametric ROM (for example, see [5, 28, 29]) and for large-scale statistical inverse problems [30–37].”
Data-driven operator inference for nonintrusive projection-based model reduction (2016, methodology): “Typically, the operators for µ are constructed from the operators for µ 1 , . . . , µ M via elementwise interpolation [44, 45, 46, 47].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “This is computationally expensive, which calls for techniques that approximate the reduced operator Ã(z) without requiring assembly of A(z) first [155, 7, 67].”