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A Bayesian Approach to the Identification Problem with Given Material Interfaces in the Darcy Flow
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SYSNO ASEP 0495898 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title A Bayesian Approach to the Identification Problem with Given Material Interfaces in the Darcy Flow Author(s) Domesová, Simona (UGN-S) ORCID, SAI, RID
Béreš, Michal (UGN-S) ORCID, RID, SAINumber of authors 2 Source Title High Performance Computing in Science and Engineering. HPCSE 2017. - Cham : Springer, 2018 / Kozubek T. - ISBN 978-3-319-97135-3 Pages s. 203-216 Number of pages 14 s. Publication form Online - E Action HPCSE 2017: International Conference on High Performance Computing in Science and Engineering /3./ Event date 22.05.2017 - 25.05.2017 VEvent location Karolinka Country CZ - Czech Republic Event type WRD Language eng - English Country CH - Switzerland Keywords Bayesian inversion ; Darcy flow ; identification problem ; Metropolis-Hastings ; posterior distribution Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects LQ1602 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) LD15105 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UGN-S - RVO:68145535 UT WOS 000469334300015 EID SCOPUS 85050458321 DOI 10.1007/978-3-319-97136-0_15 Annotation The contribution focuses on the estimation of material parameters on subdomains with given material interfaces in the Darcy flow problem. For the estimation, we use the Bayesian approach, which incorporates the natural uncertainty of measurements. The main interest of this contribution is to describe the posterior distribution of material parameters using samples generated by the Metropolis-Hastings method. This method requires a large number of direct problem solutions, which is time-consuming. We propose a combination of the standard direct solutions with sampling from the stochastic Galerkin method (SGM) solution. The SGM solves the Darcy flow problem with random parameters as additional problem dimensions. This leads to the solution in the form of a function of both random variables and space variables, which is computationally expensive to obtain, but the samples are very cheap. The resulting sampling procedure is applied to a model groundwater flow inverse problem as an alternative to the existing deterministic approach. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2019 Electronic address https://link.springer.com/content/pdf/10.1007%2F978-3-319-97136-0_15.pdf
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