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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

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QUANTIFICATION OF UNCERTAINTY FROM HIGH-DIMENSIONAL SCATTERED DATA VIA POLYNOMIAL APPROXIMATION

Volume 4, Issue 3, 2014, pp. 243-271
DOI: 10.1615/Int.J.UncertaintyQuantification.2014008084
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ABSTRACT

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high-dimensional stochastic space in the context of limited amount of information. The proposed approach involves a procedure for the selection of an approximation basis and the evaluation of the associated coefficients. The selection of the approximation basis relies on the a priori choice of the high-dimensional model representation format combined with a modified least angle regression technique. The resulting basis then provides the structure for the actual approximation basis, possibly using different functions, more parsimonious and nonlinear in its coefficients. To evaluate the coefficients, both an alternate least squares and an alternate weighted total least squares methods are employed. Examples are provided for the approximation of a random variable in a high-dimensional space as well as the estimation of a random field. Stochastic dimensions up to 100 are considered, with an amount of information as low as about 3 samples per dimension, and robustness of the approximation is demonstrated with respect to noise in the dataset. The computational cost of the solution method is shown to scale only linearly with the cardinality of the a priori basis and exhibits a (Nq)s, 2 ≤ s ≤ 3, dependence with the number Nq of samples in the dataset. The provided numerical experiments illustrate the ability of the present approach to derive an accurate approximation from scarce scattered data even in the presence of noise.

CITED BY
  1. Konakli Katerina, Sudret Bruno, Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions, Journal of Computational Physics, 321, 2016. Crossref

  2. Gorodetsky Alex, Karaman Sertac, Marzouk Youssef, A continuous analogue of the tensor-train decomposition, Computer Methods in Applied Mechanics and Engineering, 347, 2019. Crossref

  3. Gorodetsky Alex A., Jakeman John D., Gradient-based optimization for regression in the functional tensor-train format, Journal of Computational Physics, 374, 2018. Crossref

  4. Soley Micheline B., Bergold Paul, Gorodetsky Alex A., Batista Victor S., Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations, Journal of Chemical Theory and Computation, 18, 1, 2022. Crossref

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