Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity

By David Amsallem, Charbel Farhat. 2008

730 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/8d59bdef09ab9ca4ed2b72bf6d4e7f3273c6ada8

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Citations in the corpus

A method for interpolating on manifolds structural dynamics reduced‐order models (2009, methodology): “Unfortunately in all of the above and many other applications, structural dynamics models are usually parameterized, their reduced-order counterparts tend to lack robustness[12, 11] with respect to parameter changes, and the reconstruction of these small-size counterparts for each new set of paramet”
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].”
An Online Method for Interpolating Linear Parametric Reduced-Order Models (2011, methodology): “When applied to the subspaces spanned by a set of precomputed ROBs characterized by an optimal approximation property, this method was numerically shown—in the context of challenging three-dimensional computational fluid dynamics (CFD) applications—to generate new ROBs that retain this optimal appro”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “is proposed by Amsallem and Farhat [2, 1] for efficiently constructing an accurate and robust POD reduced system with respect to parameter variations.”
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows (2012, positive): “s [6, 7, 8]. Within these contexts, projection-based model-reduction methods have been successfully applied to problems in structural dynamics [3], aerodynamics [9, 10, 11, 12, 13] and aeroelasticity [14, 15, 16, 17, 18, 19], among others. On the other hand, when projection is applied to linear time”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, methodology): “Traditional methods for ROMs often lack robustness with respect to parameter changes within the systems they are representing [11], or are not cost-effective enough when trying to predict complex dynamical systems (e.”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “ROMs often lack robustness with respect to parameter changes within the systems they are representing [5], or are not cost-effective enough when trying to predict complex dynamical systems (e.g., multiscale in space and time).”
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, methodology): “(For an alternative ‘interpolation’ approach to reduced order time-parameter spaces see Amsallem and Farhat (2008); Amsallem et al .”
Stabilization of projection‐based reduced‐order models (2012, methodology): “For a given free-stream pressure p∞, the LTI system associated with the aeroelastic ROM obtained by coupling the fluid and structure ROMs (see References [28, 1, 2, 29] for details on the coupling formulation) can be written as dxr dt (t) = Ar(p∞)xr(t) =  √p∞Ar,11 Ar,12 √p∞Ar,13 p∞Ar,21 0kS×kS −Ω2”
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples (2012, neutral): “when parametric variations are considered [1].”