Solution of Inverse Problems using Bayesian Approach with Application to Estimation of Material Parameters in Darcy Flow
Result description
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.
Keywords
Bayesian statisticsCross-Entropy methodDarcy flowGaussian random fieldinverse problem
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/61989100:27240/17:10237745 RIV/61989100:27740/17:10237745
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Solution of Inverse Problems using Bayesian Approach with Application to Estimation of Material Parameters in Darcy Flow
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Electrical and Electronic Engineering
ISSN
1336-1376
e-ISSN
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Volume of the periodical
15
Issue of the periodical within the volume
2
Country of publishing house
SK - SLOVAKIA
Number of pages
9
Pages from-to
258-266
UT code for WoS article
000409044400017
EID of the result in the Scopus database
2-s2.0-85025665571
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2017