2017
DOI: 10.1016/j.cma.2017.01.033
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Bayesian sparse polynomial chaos expansion for global sensitivity analysis

Abstract: Polynomial chaos expansions are frequently used by engineers and modellers for uncertainty and sensitivity analyses of computer models. They allow representing the input/output relations of computer models. Usually only a few terms are really relevant in such a representation. It is a challenge to infer the best sparse polynomial chaos expansion of a given model input/output data set. In the present article, sparse polynomial chaos expansions are investigated for global sensitivity analysis of computer model r… Show more

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Cited by 106 publications
(64 citation statements)
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“…These indices reflect the contribution of each parameter to the variance of the model output [29]. The Sobol' indices were evaluated using a surrogate model approach based on Polynomial Chaos Expansion (PCE) [26,[41][42][43][44].…”
Section: Global Sensitivity Analysismentioning
confidence: 99%
“…These indices reflect the contribution of each parameter to the variance of the model output [29]. The Sobol' indices were evaluated using a surrogate model approach based on Polynomial Chaos Expansion (PCE) [26,[41][42][43][44].…”
Section: Global Sensitivity Analysismentioning
confidence: 99%
“…Our DNNs are constructed using the open-source Keras [5] Python package which is built on top of the open-source Tensorflow DL library [1]. The two other methods are perhaps the most popular emulation techniques in engineering and the geosciences: Gaussian processes [GPs,32] and polynomial chaos expansion [PCE, see, e.g., 9,41,3,25,36, just to list a few]. In both cases we use state-of-the-art open source implementations: the GPflow Python package [29] for GPs, which is built on top of Tensorflow, and the Chaospy Python package [7] for PCE.…”
Section: Introductionmentioning
confidence: 99%
“…Another way of finding the coefficients is by regression method, which utilizes a finite set of MCS results to evaluate the unknown coefficients. This process is known as nonintrusive method . However, in both the methods, as the number of random variables or the order of expansion increases, the size of the system matrix increases exponentially.…”
Section: Introductionmentioning
confidence: 99%
“…Blatman and Sudret considered a hyperbolic PC, where the higher‐order cross terms between two random variables are omitted. Blatman and Sudret and Shao et al considered a sensitivity analysis by allowing a tolerance limit to evaluate the dominant terms of PC expansion and obtain a global sparsity. Thus, construction of sparse PC is not a straightforward procedure and requires additional postprocessing.…”
Section: Introductionmentioning
confidence: 99%
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