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International Journal for Uncertainty Quantification

Published 6 issues per year

ISSN Print: 2152-5080

ISSN Online: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

Indexed in

AN OPTIMAL SAMPLING RULE FOR NONINTRUSIVE POLYNOMIAL CHAOS EXPANSIONS OF EXPENSIVE MODELS

Volume 5, Issue 3, 2015, pp. 275-295
DOI: 10.1615/Int.J.UncertaintyQuantification.2015008446
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ABSTRACT

In this work we present the optimized stochastic collocation method (OSC). OSC is a new sampling rule that can be applied to polynomial chaos expansions (PCE) for uncertainty quantification. Given a model function, the goal of PCE is to find the polynomial from a given polynomial space that is closest to the model function with respect to the L2-norm induced by a given probability measure. Many PCE methods approximate the involved projection integral by discretization with a finite set of integration points. Our key idea is to choose these integration points through numerical optimization based on an operator norm derived from the discretized projection operator. OSC is a generalization of Gaussian quadrature: both methods coincide for one-dimensional integration and under appropriate problem settings in multidimensional problems. As opposed to many established integration rules, OSC does not generally lead to tensor grids in multidimensional problems. With OSC, the user can specify the number of integration points independently of the problem dimension and PCE expansion order. This allows one to reduce the number of model evaluations and still achieve a high accuracy. The input parameters can follow any kind of probability distribution, as long as the statistical moments up to a certain order are available. Even statistically dependent parameters can be handled in a straightforward and natural fashion. Moreover, OSC allows reusing integration points, if results from earlier model evaluations are available. Gauss-Kronrod and Stroud integration rules can be reproduced with OSC for the respective special cases.

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  2. Oladyshkin Sergey, Nowak Wolfgang, Incomplete statistical information limits the utility of high-order polynomial chaos expansions, Reliability Engineering & System Safety, 169, 2018. Crossref

  3. Paulson Joel A., Mesbah Ali, Nonlinear Model Predictive Control with Explicit Backoffs for Stochastic Systems under Arbitrary Uncertainty, IFAC-PapersOnLine, 51, 20, 2018. Crossref

  4. Köppel Markus, Franzelin Fabian, Kröker Ilja, Oladyshkin Sergey, Santin Gabriele, Wittwar Dominik, Barth Andrea, Haasdonk Bernard, Nowak Wolfgang, Pflüger Dirk, Rohde Christian, Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario, Computational Geosciences, 23, 2, 2019. Crossref

  5. Massoud Elias C., Emulation of environmental models using polynomial chaos expansion, Environmental Modelling & Software, 111, 2019. Crossref

  6. Paulson Joel A., Martin-Casas Marc, Mesbah Ali, Optimal Bayesian experiment design for nonlinear dynamic systems with chance constraints, Journal of Process Control, 77, 2019. Crossref

  7. Paulson Joel A., Martin-Casas Marc, Mesbah Ali, Mendes Pedro, Fast uncertainty quantification for dynamic flux balance analysis using non-smooth polynomial chaos expansions, PLOS Computational Biology, 15, 8, 2019. Crossref

  8. Makrygiorgos Georgios, Maggioni Giovanni Maria, Mesbah Ali, Surrogate modeling for fast uncertainty quantification: Application to 2D population balance models, Computers & Chemical Engineering, 138, 2020. Crossref

  9. van den Bos Laurent, Sanderse Benjamin, Bierbooms Wim, van Bussel Gerard, Generating Nested Quadrature Rules with Positive Weights based on Arbitrary Sample Sets, SIAM/ASA Journal on Uncertainty Quantification, 8, 1, 2020. Crossref

  10. Litvinenko Alexander, Logashenko Dmitry, Tempone Raul, Wittum Gabriel, Keyes David, Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability, GEM - International Journal on Geomathematics, 11, 1, 2020. Crossref

  11. Bonzanini Angelo D., Paulson Joel A., Makrygiorgos Georgios, Mesbah Ali, Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks, Computers & Chemical Engineering, 145, 2021. Crossref

  12. Paulson Joel A., Mesbah Ali, Shaping the Closed-Loop Behavior of Nonlinear Systems Under Probabilistic Uncertainty Using Arbitrary Polynomial Chaos, 2018 IEEE Conference on Decision and Control (CDC), 2018. Crossref

  13. Rodrigues Diogo, Makrygiorgos Georgios, Mesbah Ali, Tractable Global Solutions to Bayesian Optimal Experiment Design, 2020 59th IEEE Conference on Decision and Control (CDC), 2020. Crossref

  14. Litvinenko Alexander, Logashenko Dmitry, Tempone Raul, Wittum Gabriel, Keyes David, Propagation of Uncertainties in Density-Driven Flow, in Sparse Grids and Applications - Munich 2018, 144, 2021. Crossref

  15. Lototsky S. V., Mikulevicius R., Rozovsky B. L., Intrusive and non-intrusive chaos approximation for a two-dimensional steady state Navier–Stokes system with random forcing, Stochastics and Partial Differential Equations: Analysis and Computations, 2022. Crossref

  16. Chen Yaqian, Ghori Muhammad Bilal, Kang Yanmei, Bifurcation Analysis of Brain Connectivity Regulated Neural Oscillations in Schizophrenia, International Journal of Bifurcation and Chaos, 32, 11, 2022. Crossref

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