A Bayesian Approach to the Identification Problem with Given Material Interfaces in the Darcy Flow
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.
KeywordsBayesian inversion Darcy flow Metropolis-Hastings Identification problem Posterior distribution Uncertainty quantification
This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science - LQ1602”. The work was also partially supported by EU under the COST programme Action IC1305 “Network for Sustainable Ultrascale Computing (NESUS)” and by the project LD15105 “Ultrascale computing in geo-sciences”. The authors were also supported by Grant of SGS No. SP2017/56, VŠB - Technical University of Ostrava, Czech Republic.
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