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A Bayesian Approach to the Identification Problem with Given Material Interfaces in the Darcy Flow

  1. 1.
    0495898 - ÚGN 2019 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
    Domesová, Simona - Béreš, Michal
    A Bayesian Approach to the Identification Problem with Given Material Interfaces in the Darcy Flow.
    High Performance Computing in Science and Engineering. HPCSE 2017. Cham: Springer, 2018 - (Kozubek, T.), s. 203-216. Lecture Notes in Computer Science, Code 216349, Volume 11087. ISBN 978-3-319-97135-3.
    [HPCSE 2017: International Conference on High Performance Computing in Science and Engineering /3./. Karolinka (CZ), 22.05.2017-25.05.2017]
    Grant CEP: GA MŠMT LQ1602; GA MŠMT LD15105
    Institucionální podpora: RVO:68145535
    Klíčová slova: Bayesian inversion * Darcy flow * identification problem * Metropolis-Hastings * posterior distribution
    Obor OECD: Applied mathematics
    https://link.springer.com/content/pdf/10.1007%2F978-3-319-97136-0_15.pdf

    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.
    Trvalý link: http://hdl.handle.net/11104/0288772

     
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