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International Journal for Uncertainty Quantification

Publication de 6  numéros par an

ISSN Imprimer: 2152-5080

ISSN En ligne: 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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A GRADIENT-BASED SAMPLING APPROACH FOR DIMENSION REDUCTION OF PARTIAL DIFFERENTIAL EQUATIONS WITH STOCHASTIC COEFFICIENTS

Volume 5, Numéro 1, 2015, pp. 49-72
DOI: 10.1615/Int.J.UncertaintyQuantification.2014010945
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RÉSUMÉ

We develop a projection-based dimension reduction approach for partial differential equations with high-dimensional stochastic coefficients. This technique uses samples of the gradient of the quantity of interest (QoI) to partition the uncertainty domain into "active" and "passive" subspaces. The passive subspace is characterized by near-constant behavior of the quantity of interest, while the active subspace contains the most important dynamics of the stochastic system. We also present a procedure to project the model onto the low-dimensional active subspace that enables the resulting approximation to be solved using conventional techniques. Unlike the classical Karhunen-Loeve expansion, the advantage of this approach is that it is applicable to fully nonlinear problems and does not require any assumptions on the correlation between the random inputs. This work also provides a rigorous convergence analysis of the quantity of interest and demonstrates: at least linear convergence with respect to the number of samples. It also shows that the convergence rate is independent of the number of input random variables. Thus, applied to a reducible problem, our approach can approximate the statistics of the QoI to within desired error tolerance at a cost that is orders of magnitude lower than standard Monte Carlo. Finally, several numerical examples demonstrate the feasibility of our approach and are used to illustrate the theoretical results. In particular, we validate our convergence estimates through the application of this approach to a reactor criticality problem with a large number of random cross-section parameters.

CITÉ PAR
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  2. Gunzburger Max, Webster Clayton G., Zhang Guannan, Sparse Collocation Methods for Stochastic Interpolation and Quadrature, in Handbook of Uncertainty Quantification, 2017. Crossref

  3. Stoyanov Miroslav, Seleson Pablo, Webster Clayton, A surrogate modeling approach for crack pattern prediction in peridynamics, 19th AIAA Non-Deterministic Approaches Conference, 2017. Crossref

  4. Stoyanov Miroslav, Adaptive Sparse Grid Construction in a Context of Local Anisotropy and Multiple Hierarchical Parents, in Sparse Grids and Applications - Miami 2016, 123, 2018. Crossref

  5. Holodnak John T., Ipsen Ilse C. F., Smith Ralph C., A Probabilistic Subspace Bound with Application to Active Subspaces, SIAM Journal on Matrix Analysis and Applications, 39, 3, 2018. Crossref

  6. Gunzburger Max, Webster Clayton G., Zhang Guannan, Sparse Collocation Methods for Stochastic Interpolation and Quadrature, in Handbook of Uncertainty Quantification, 2015. Crossref

  7. Coleman Kayla D., Lewis Allison, Smith Ralph C., Williams Brian, Morris Max, Khuwaileh Bassam, Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics, SIAM/ASA Journal on Uncertainty Quantification, 7, 1, 2019. Crossref

  8. Ghauch Ziad G., Leveraging Adapted Polynomial Chaos Metamodels for Real-Time Bayesian Updating, Journal of Verification, Validation and Uncertainty Quantification, 4, 4, 2019. Crossref

  9. Morrow Zachary, Stoyanov Miroslav, A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions, SIAM Journal on Scientific Computing, 42, 4, 2020. Crossref

  10. Abdurrahman Muhammad Hafizh, Irawan Budhi, Setianingsih Casi, A Review of Light Gradient Boosting Machine Method for Hate Speech Classification on Twitter, 2020 2nd International Conference on Electrical, Control and Instrumentation Engineering (ICECIE), 2020. Crossref

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