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Solution of Inverse Problems using Bayesian Approach with Application to Estimation of Material Parameters in Darcy Flow

  1. 1. 0482833 - UGN-S 2018 RIV SK eng J - Článek v odborném periodiku
    Domesová, Simona - Beres, Michal
    Solution of Inverse Problems using Bayesian Approach with Application to Estimation of Material Parameters in Darcy Flow.
    Advances in Electrical and Electronic Engineering. Roč. 15, č. 2 (2017), s. 258-266 ISSN 1336-1376
    Grant CEP: GA MŠk LQ1602
    Institucionální podpora: RVO:68145535
    Klíčová slova: Bayesian statistics * Cross-Entropy method * Darcy flow * Gaussian random field * inverse problem
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Applied mathematics
    http://advances.utc.sk/index.php/AEEE/article/view/2236

    Standard numerical methods for solving inverse problems in partial differential equations do not reflect a possible inaccuracy in observed data. However, in real engineering applications we cannot avoid uncertainties caused by measurement errors. In the Bayesian approach every unknown or inaccurate value is treated as a random variable. This paper presents an application of the Bayesian inverse approach to the reconstruction of a porosity field as a parameter of the Darcy flow problem. However, this framework can be applied to a wide range of problems that involve some amount of uncertainty. Here the material field is modeled as a Gaussian random field, which is expressed as a function of several random variables. The information about these random variables is given by the resulting posterior distribution, which is then studied using the Cross-Entropy method and samples are generated using the Metropolis-Hastings algorithm.
    Trvalý link: http://hdl.handle.net/11104/0278233
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