Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

By Géraud Blatman, Bruno Sudret. Reliability Engineering & System Safety, 2010

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Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, background): “Since then, a number of other studies have used PCEs for the estimation of variance-based sensitivity indices (e.g., Blatman and Sudret, 2010; Sochala and Le Maître, 2013; Garcia-Cabrejo and Valocchi, 2014).”
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012, methodology): “The recent paper [4] explores sparse and partially random integration techniques for PCE, applied to sensitivity analysis, and provides Monte Carlo based estimates for the error introduced by the random character of the used integration rules.”
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): “Sometimes, a much smaller number M can be found by a sparse selection [5] of the relevant terms in Eq.”
Polynomial-Chaos-based Kriging (2015, positive): “Such a truncation scheme corresponds to a set of multi-indexes α ∈ A ⊂ N M such that the system response is accurately approximated with respect to some error measure Blatman and Sudret (2010a, 2011): There are several ways to select a priori a truncation set A .”