Abonnement à la biblothèque: Guest
Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections
International Journal for Uncertainty Quantification
Facteur d'impact: 3.259 Facteur d'impact sur 5 ans: 2.547 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

Ouvrir l'accès

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018020215
pages 43-59

CLUSTERING-BASED COLLOCATION FOR UNCERTAINTY PROPAGATION WITH MULTIVARIATE DEPENDENT INPUTS

Anne W. Eggels
Centrum Wiskunde & Informatica, Amsterdam, the Netherlands
D. T. Crommelin
Centrum Wiskunde & Informatica, Amsterdam, the Netherlands; Korteweg−de Vries Institute for Mathematics, University of Amsterdam, the Netherlands
J. A. S. Witteveen
Centrum Wiskunde & Informatica, Amsterdam, the Netherlands

RÉSUMÉ

In this paper, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend the use of collocation methods to uncertainty propagation with multivariate, dependent input, in which the output approximation is piecewise constant on the clusters. The approach is particularly useful in situations where the probability distribution of the input is unknown and only a sample from the input distribution is available. We examine several clustering methods and assess the convergence of collocation based on these methods both theoretically and numerically. We demonstrate good performance of the proposed methods, most notably for the challenging case of nonlinearly dependent inputs in higher dimensions. Numerical tests with input dimension up to 16 are included, using as benchmarks the Genz test functions and a test case from computational fluid dynamics (lid-driven cavity flow).


Articles with similar content:

PROPAGATION OF UNCERTAINTY BY SAMPLING ON CONFIDENCE BOUNDARIES
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 5
Jan Peter Hessling, Thomas Svensson
DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 1
Bert J. Debusschere, Habib N. Najm, Peter Thornton, Cosmin Safta, Khachik Sargsyan, Daniel Ricciuto
Three-Dimensional Reconstruction of Statistically Optimal Unit Cells of Multimodal Particulate Composites
International Journal for Multiscale Computational Engineering, Vol.8, 2010, issue 5
D. Rypl, B. C. Collins, Karel Matous
LOW-COST MULTI-DIMENSIONAL GAUSSIAN PROCESS WITH APPLICATION TO UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 4
Guang Lin, Bledar A. Konomi
EMPIRICAL EVALUATION OF BAYESIAN OPTIMIZATION IN PARAMETRIC TUNING OF CHAOTIC SYSTEMS
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 6
Antti Solonen, Heikki Jarvinen, Janne Hakkarainen, Mudassar Abbas, Erkki Oja, Alexander Ilin