Modeling uncertainty in flow simulations via generalized polynomial chaos

By Dongbin Xiu, G. Em Karniadakis. 2003

1,525 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/947ccd0038877362ca3ab9f1a1e32528ca0312cd

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In Aerospace Engineering

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations (2013, result): “, [60]) in comparison to classical PCE techniques, when applied to input distributions that fall outside the range of classical [88] or generalized version [93] of the PCE.”
A new stochastic approach to transient heat conduction modeling with uncertainty (2003, background): “For more details about generalized polynomial chaos, see [35,36,37].”
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012, methodology): “The best-known method fro m this group is the stochastic Galerkin technique, which orig inated from structural mechanics [20] and has been applied in studies for modeling uncertainties in flow problems ([19], [ 30], [58]).”
Sparse grid collocation schemes for stochastic natural convection problems (2007, background): “Karniadakis and co-workers applied a generalized polynomial chaos expansion to model uncertainty in diffusion [11], fluid flow applications [12] and transient heat conduction problems [13].”
A reduced spectral function approach for the stochastic finite element analysis (2011, methodology): “The same idea can be extended to non-Gaussian random variables, provided more generalized functional basis are used [10–12] so that the orthonormality with respect to the probability density functions can be retained.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, methodology): “More details of the computations including other types of random boundary conditions as well as numerical formulations can be found in [92].”
Inverse Problems in Heat Transfer (2009, methodology): “In more recent work [30, 32] uses the generalized Askey system of orthogonal polynomials [46] as trial bases for the probability space.”
Stochastic approaches to uncertainty quantification in CFD simulations (2005, methodology): “/ Stochastic CFD The eigenvalue problem has the solution [26] 2b~r 2 ,ki , (2.”
Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos (2007, methodology): “Generalized polynomial chaos and multi-element generalized polynomial chaos have been applied by Karniadakis and co-workers to for example flow problems and fluid–structure interaction problems in [28–31].”
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification (2018, neutral): “Popular choices for surrogate models in the literature include, Gaussian processes [11, 12, 13, 14, 15], polynomial chaos expansions [16, 17, 18, 19], radial basis functions [20] and relevance vector machines [21].”
A comparative study of uncertainty propagation methods for black-box-type problems (2008, background): “It is reported that the convergence rate of PCE is not fast when the inputs are non-normal and a generalized PCE (Xiu and Karniadakis 2003) has been proposed to solve this problem with various orthogonal polynomials in Askey scheme.”