Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach

By Géraud Blatman, Bruno Sudret. 2008

298 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/09a57a375450d4f44d8859f71b7fd37fe6ee1ecb

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In Civil and Structural Engineering

In Statistics and Probability

Citations in the corpus

Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems (2010, background): “regression [ 6 ] or Galerkin projections [2, 16, 18, 35].”
Polynomial-Chaos-based Kriging (2015, unknown): “Further developments which combine spectral expansions and compressive sensing ideas have lead to so-called sparse polynomial chaos expansions Blatman and Sudret (2008, 2010a,b); Doostan and Owhadi (2011); Blatman and Sudret (2011); Doostan et al. (2013); Jakeman et al. (2014).”
Reliability-based design optimization using kriging surrogates and subset simulation (2011, background): “…and Bourgund, 1990; Kim and Na, 1997; Das and Zheng, 2000), polynomial chaos expansions (Sudret and Der Kiureghian, 2002; Berveiller et al., 2006; Blatman and Sudret, 2008, 2010), support vector machines (Hurtado, 2004; Deheeger, 2008; Bourinet et al., 2010), neural networks (Papadrakakis and…”
A new adaptive response surface method for reliability analysis (2013, methodology): “This new model, called metamodel, can be of various kinds: quadratic response surfaces [21], polynomial chaos [23,6], kriging [40,27], neural network [36,13,20] or even support vector machine [25].”
Adaptive sparse polynomial chaos expansion based on least angle regression (2011, methodology): “An iterative procedure based on stepwise regression has been proposed in [40, 20] to circumvent this difficulty.”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, background): “quadrature points and weights for the yk and ωk (or a subset of these points), ... The reader can refer to [14 ]f or a detailed study of these different choices (accuracy of the solution, impact on the condition number of the linear system, ... ). A methodology for the adaptive construction of funct”
Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes (2016, unknown): “In order to ﬁnd directly the signiﬁcant polynomials and associated coeﬃcients, sparse PCE have been introduced recently by Blatman and Sudret [10, 11]; Bieri and Schwab [8].”
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2010, methodology): “A first algorithm has been recently proposed in [34].”
Polynomial chaos expansion in structural dynamics: Accelerating the convergence of the first two statistical moment sequences (2015, background): “Several novel approaches have been developed to address the issue of computational cost, see for example [19–23].”
eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces (2010, methodology): “A rst way to solve a PDE de ned on a random domain consists in using direct spectral stochastic approaches (interpolation [8, 9, 10, 11, 12], projection [13, 14, 15], regression [16]), or any other direct stochastic method such as Monte-Carlo or quasi Monte-Carlo simulations [17], coupled with a det”