Polynomial chaos expansion for sensitivity analysis

By Thierry Crestaux, O. L. Le Maître, Jean-Marc Martinez. Reliability Engineering & System Safety, 2009

772 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/063ddd94bdb01a22935fefece1ac43ab1fe1facf

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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, background): “Because the reduced model is merely a polynomial and has exploitable properties due to the orthogonal basis, it is vastly faster than the original one and offers a large playground for stochastic analysis [24, 57, 85], risk assessment [58, 84], and global sensitivity analysis [10, 57, 79].”
Global sensitivity analysis: a flexible and efficient framework with an example from stochastic hydrogeology (2012, methodology): “PCE has already been used for sensitivity analysis in different fields of applications [3,12,13].”
Reliability in composites – a selective review and survey of current development (2012, background): “These new advances have been carried out in an effort to generate statistics from a response vector for each node [51,52].”
Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes (2016, neutral): “[19]; Buzzard and Xiu [16]; Buzzard [15]) and sparse polynomial expansions (e.”
Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives] (2013, methodology): “Sensitivity analysis [36] aiming at quantifying dominant sources of uncertainty has been studied with regard to the application of PCEs [7], [37].”
Numerical assessment of metamodelling strategies in computationally intensive optimization (2012, background): “Some examples of such techniques include: polynomials (Crestaux et al., 2009; Fen et al., 2009; Hussain et al., 2002; Sudret, 2008), kriging which is sometimes called design and analysis of computer experiment (DACE) in the metamodelling context (Kleijnen, 2005; Sacks et al., 1989; Sakata et al.,…”
Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics (2020, background): “of aPCE, the sensitivity indices can be calculated analytically [47, 56].”
Polynomial Chaos expansion for subsurface flows with uncertain soil parameters (2013, methodology): “For example, sensitivity indices are readily obtained from the PCE of the outputs (Crestaux et al. 2009).”
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012, background): “Recently, the sensitivity analysis b ased on PCE decomposition [5], [9], [34] has received increased att ention.”
Machine Learning in Aerodynamic Shape Optimization (2022, methodology): “For example, the orthogonal bases-based polynomial chaos expansion (PCE) [158, 159] provides analytical mean and standard deviation of the whole model observations, as well as the Sobol’ indices for sensitivity analysis [160, 161].”
Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions (2017, methodology): “In PCE, the variance-based Sobol’ sensitivity indices can be extracted by gathering expansion coefficients of the constructed PCE according to the dependency of each basis polynomial (Crestaux et al. 2009; Garcia-Cabrejo and Valocchi 2014; Sudret 2008).”
Probabilistic assessment of seawater intrusion under multiple sources of uncertainty (2015, methodology): “This approach allows obtaining a surrogate model for a given quantity of interest and enables one to calculate the Sobol indices analytically via a straightforward post-processing analysis (e.g. [12,38]).”