Numerical realization of the Bayesian inversion accelerated using surrogate models

0571878 - ÚGN 2024 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Bérešová, Simona
Numerical realization of the Bayesian inversion accelerated using surrogate models.
Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar. Praha: Institute of Mathematics CAS Prague, 2023 - (Chleboun, J.; Kůs, P.; Papež, J.; Rozložník, M.; Segeth, K.; Šístek, J.), s. 25-36. ISBN 978-80-85823-73-8.
[Programs and Algorithms of Numerical Mathematics /21./. Jablonec nad Nisou (CZ), 19.06.2022-24.06.2022]
Grant CEP: GA TA ČR(CZ) TK02010118
Institucionální podpora: RVO:68145535
Klíčová slova: Bayesian inversion * delayed-acceptance Metropolis-Hastings * Markov chain Monte Carlo * surrogate model
Obor OECD: Applied mathematics
https://dml.cz/bitstream/handle/10338.dmlcz/703185/PANM_21-2022-1_6.pdf

The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte Carlo (MCMC) methods accelerated with surrogate models. A surrogate model is understood as an approximation of the forward model which should be computationally much cheaper. The target distribution is not fully replaced by its approximation. Therefore, samples from the exact posterior distribution are provided. In addition, non-intrusive surrogate models can be updated during the sampling process resulting in an adaptive MCMC method. The use of the surrogate models significantly reduces the number of evaluations of the forward model needed for a reliable description of the posterior distribution. Described sampling procedures are implemented in the form of a Python package.
Trvalý link: https://hdl.handle.net/11104/0342777