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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

VARIABLE-SEPARATION BASED ITERATIVE ENSEMBLE SMOOTHER FOR BAYESIAN INVERSE PROBLEMS IN ANOMALOUS DIFFUSION REACTION MODELS

Volume 9, Issue 3, 2019, pp. 245-273
DOI: 10.1615/Int.J.UncertaintyQuantification.2019028759
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ABSTRACT

The iterative ensemble smoother (IES) has been widely used to estimate parameters and states of dynamic models where the data are collected at all observation steps simultaneously. A large number of IES ensemble samples may be required in the estimation. This implies that we need to repeatedly compute the forward model corresponding to the ensemble samples. This leads to slow efficiency for large-scale and strongly nonlinear models. To accelerate the posterior inference in the estimation, a low rank approximation using a variable-separation (VS) method is presented to reduce the cost of computing the forward model. It will be efficient to construct a surrogate model based on the low rank approximation, which gives a separated representation of the solution for the stochastic partial differential equations (SPDEs). The separated representation is the product of deterministic basis functions and stochastic basis functions. For the anomalous diffusion reaction equations, the solution of the next moment depends on all of the previous moments, and this causes expensive computation for the Bayesian inverse problem. The presented VS can avoid this process through a few deterministic basis functions. The surrogate model can work well as the iteration moves on because the stochastic basis becomes more accurate when the uncertainty of random parameters decreases. To enhance the applicability in Bayesian inverse problems, we apply the VS-based IES method to complex structure patterns, which can be parameterized by discrete cosine transform (DCT). The post-processing technique based on a regularization method is employed after the iterations to improve the connectivity of the main features. In the paper, we focus on the time fractional diffusion reaction models in porous media and investigate their Bayesian inverse problems using the VS-based IES. A few numerical examples are presented to show the performance of the proposed IES method by taking account of structure inversion in permeability fields, parameters in permeability and reaction fields, and source functions.

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CITED BY
  1. Ba Yuming, Jiang Lijian, A two-stage variable-separation Kalman filter for data assimilation, Journal of Computational Physics, 434, 2021. Crossref

  2. Ba Yuming, Jiang Lijian, A residual-driven adaptive Gaussian mixture approximation for Bayesian inverse problems, Journal of Computational and Applied Mathematics, 399, 2022. Crossref

  3. Alzahrani Hasnaa H, Lucchesi Marco, Mustapha Kassem, Le Maître Olivier P, Knio Omar M, Bayesian calibration of order and diffusivity parameters in a fractional diffusion equation, Journal of Physics Communications, 5, 8, 2021. Crossref

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