Stochastic model reduction for chaos representations

By Alireza Doostan, Roger G. Ghanem, John R. Red-Horse. 2007

209 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3af0d5e8d8ec74c221cbbfba328b98d40a343137

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In Civil and Structural Engineering

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, methodology): “These developments include adaptive polynomial degree and sparse truncations of the PC basis [34, 75], and other methods of stochastic model reduction [76].”
POD-DEIM model order reduction for strain softening viscoplasticity (2017, methodology): “In the field of solid mechanics, MOR techniques such as POD-G [12,13], Karhunen Loeve Expansion [14,15], and Proper Generalized Decomposition (PGD) [16,17] are employed to reduce the dimension of the system of equations.”
The stochastic finite element method: Past, present and future (2009, unknown): “[1–3,19,22,28,29,41,66,67, 94,108,113,187,189].”
Variance decomposition and global sensitivity for structural systems (2010, methodology): “[3] used stochastic model reduction for chaos representations, and, moreover, used stochastic model reduction by constructing a coarse-scale from a specified fine-scale whose probabilistic structure can be accurately determined [4].”
Non-intrusive low-rank separated approximation of high-dimensional stochastic models (2012, background): “ number of recent techniques have been proposed that exploit, for instance, low-rank or sparsity structures of quantities of interest in order to reduce this exponential complexity growth, see, e.g., [23, 70, 57, 11, 49, 10, 12, 27, 58, 25]. However, eﬀective treatment of the curse-of-dimensionality”
Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos (2013, methodology): “Although not yet applied in astrodynamics, previous research using PC includes uncertainty quantification in engineering fields such as: fluid dynamics [11–18], solid mechanics [19–22], multibody dynamics [23,24], high-order state estimation [25,26], and many other applications.”
Uncertainty analysis of complex structural systems (2009, methodology): “The efficiency of the solution shown in [15, 16] was compared with direct MCS.”
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007, background): “On the other hand the works [22, 47] (see also the references therein) have pursued generalized spectral decompositions for approximation, seeking reduced bases that are tailored to the solution and which seem to be rather promising.”
Surrogate accelerated sampling of reservoir models with complex structures using sparse polynomial chaos expansion (2015, methodology): “Among them are the multi-scale model reduction of [57] and the sparse decomposition of [60, 59, 58] for the stochastic Galerkin technique, anisotropic and adaptive sparse grids of [51, 62, 61] for the stochastic collocation scheme, and low-rank solution approximations of [63, 64, 65, 78].”
A non-adapted sparse approximation of PDEs with stochastic inputs (2010, methodology): “Among them are the multi-scale model reduction of [33] and the sparse decomposition of [60,8,6,7] for the stochastic Galerkin technique, adaptive sparse regression approaches of [10,11] for PC expansions, anisotropic and adaptive sparse grids of [50,44] for the stochastic collocation scheme, and the”
A least-squares approximation of partial differential equations with high-dimensional random inputs (2009, unknown): “Model reduction techniques have been developed in [7,10,22,21] to reduce this drawback for the case of stochastic Galerkin schemes.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “1), and the examples are for linear problems, the gPC framework can be readily applied to complex problems including the time-dependent and nonlinear ones, for example, Burgers’ equation [34, 94], fluid dynamics [40, 41, 44, 46, 92], flow-structure interactions [96], hyperbolic problems [11,31], mat”