Abstract
The contribution is motivated by the Bayesian approach to the solution of material identification problems which frequently appear in geo-engineering. We shall consider the cases with associated forward model describing flow in porous media with or without fractures as well as coupled hydro-mechanical processes. When assuming uncertainties in observed data, the use of the Bayesian inversion is natural. In comparison to deterministic methods, which lead only to a point estimate of the identified parameters, the Bayesian approach provides their probability distribution. The implementation of the Bayesian inversion is realized via Markov Chain Monte Carlo methods. The paper aims at the acceleration of the posterior sampling using a surrogate model that provides a polynomial approximation of the full forward model. The sampling procedure is based on the delayed acceptance Metropolis-Hastings (DAMH) algorithm. Therefore, for each proposed sample, the acceptance decision contains a preliminary step, which works only with an approximated posterior distribution constructed using the surrogate model. Furthermore, the approximated posterior distribution is being updated using new snapshots obtained during the sampling process. The posterior distribution updates are realized via updates of the surrogate model. The application of the described approach is shown through several model examples including flow in porous media with fractures and hydro-mechanical coupling.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Robert, C., Casella, G.: Monte Carlo Statistical Methods. Springer-Verlag, New York (2004)
Christen, J.A., Fox, C.: Markov chain Monte Carlo using an approximation. J. Comput. Graph. Stat. 14(4) (2005)
Domesová, S.: The use of radial basis function surrogate models for sampling process acceleration in Bayesian inversion. In: AETA 2018. Lecture Notes in Electrical Engineering, vol. 554. Springer, Cham (2018)
Roberts, G.O., Rosenthal, J.S.: Examples of adaptive MCMC. J. Comput. Graph. Stat. 18(2), 349–367 (2009)
Cui, T., Fox, C., O’Sullivan, M.J.: Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm. Water Resour. Res. 47(10) (2011)
Blaheta, R., Béreš, M., Domesová, S., Horák, D.: Bayesian inversion for steady flow in fractured porous media with contact on fractures and hydro-mechanical coupling. Accepted (2020)
Blaheta, R., Béreš, M., Domesová, S., Pan, P.: A comparison of deterministic and Bayesian inversion with application in micromechanics. Appl. Math. 63(6) (2018)
Domesová, S., Béreš, M.: A Bayesian approach to the identification problem with given material interfaces in the Darcy flow. In: HPCSE 2017. LNSC, vol. 11087 (2018)
Acknowledgements
This work was supported by the project TK02010118 funded by Technology Agency of the Czech Republic.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Domesová, S., Béreš, M., Blaheta, R. (2021). Efficient Implementation of the Bayesian Inversion by MCMC with Acceleration of Posterior Sampling Using Surrogate Models. In: Barla, M., Di Donna, A., Sterpi, D. (eds) Challenges and Innovations in Geomechanics. IACMAG 2021. Lecture Notes in Civil Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-030-64514-4_91
Download citation
DOI: https://doi.org/10.1007/978-3-030-64514-4_91
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-64513-7
Online ISBN: 978-3-030-64514-4
eBook Packages: EngineeringEngineering (R0)