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Polynomial chaos expansion of a multimodal random vector

Abstract : A methodology and algorithms are proposed for constructing the polynomial chaos expansion (PCE) of multimodal random vectors. An algorithm is developed for generating independent realizations of any multimodal multivariate probability measure that is constructed from a set of independent realizations using the Gaussian kernel-density estimation method. The PCE is then performed with respect to this multimodal probability measure, for which the realizations of the polynomial chaos are computed with an adapted algorithm. Finally, a numerical application is presented for analyzing the convergence properties.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01105959
Contributor : Christian Soize <>
Submitted on : Tuesday, January 20, 2015 - 1:01:38 PM
Last modification on : Thursday, March 19, 2020 - 11:52:03 AM
Long-term archiving on: : Tuesday, April 21, 2015 - 10:48:54 AM

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Christian Soize. Polynomial chaos expansion of a multimodal random vector. SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2015, 3 (1), pp.34 - 60. ⟨10.1137/140968495⟩. ⟨hal-01105959⟩

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