Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport
Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of th...
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MDPI AG
2021-08-01
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1974 |
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| author | Vasiliy V. Grigoriev Petr N. Vabishchevich |
| author_facet | Vasiliy V. Grigoriev Petr N. Vabishchevich |
| author_sort | Vasiliy V. Grigoriev |
| collection | DOAJ |
| description | Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals. |
| first_indexed | 2024-03-10T08:37:30Z |
| format | Article |
| id | doaj.art-d28737f6166a420db4df1bbd2d7320c9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:30Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d28737f6166a420db4df1bbd2d7320c92023-11-22T08:34:40ZengMDPI AGMathematics2227-73902021-08-01916197410.3390/math9161974Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale TransportVasiliy V. Grigoriev0Petr N. Vabishchevich1Multiscale Model Reduction Laboratory, North-Eastern Federal University, 58 Belinskogo St., 677000 Yakutsk, RussiaMultiscale Model Reduction Laboratory, North-Eastern Federal University, 58 Belinskogo St., 677000 Yakutsk, RussiaStochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals.https://www.mdpi.com/2227-7390/9/16/1974uncertainty quantificationparameter identificationBayesian inferenceMarkov chain Monte Carloporous mediafinite element method |
| spellingShingle | Vasiliy V. Grigoriev Petr N. Vabishchevich Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport Mathematics uncertainty quantification parameter identification Bayesian inference Markov chain Monte Carlo porous media finite element method |
| title | Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport |
| title_full | Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport |
| title_fullStr | Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport |
| title_full_unstemmed | Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport |
| title_short | Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport |
| title_sort | bayesian estimation of adsorption and desorption parameters for pore scale transport |
| topic | uncertainty quantification parameter identification Bayesian inference Markov chain Monte Carlo porous media finite element method |
| url | https://www.mdpi.com/2227-7390/9/16/1974 |
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