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

0482833 - ÚGN 2018 RIV SK eng J - Journal Article
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
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : Bayesian statistics * Cross-Entropy method * Darcy flow * Gaussian random field * inverse problem
OECD category: 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.
Permanent Link: http://hdl.handle.net/11104/0278233