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Original title:
Numerical realization of the Bayesian inversion accelerated using surrogate models
Authors: Bérešová, Simona
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /21./, Jablonec nad Nisou (CZ), 20220619
Year: 2023
Language: eng
Abstract: 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.
Keywords: Bayesian inversion; delayed-acceptance Metropolis-Hastings; Markov chain Monte Carlo; surrogate model
Project no.: TK02010118
Funding provider: GA TA ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar, ISBN 978-80-85823-73-8
Institution: Institute of Geonics AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: https://dml.cz/bitstream/handle/10338.dmlcz/703185/PANM_21-2022-1_6.pdf
Original record: https://hdl.handle.net/11104/0342777
Permalink: http://www.nusl.cz/ntk/nusl-524977
The record appears in these collections:
Research > Institutes ASCR > Institute of Geonics
Conference materials > Papers
Authors: Bérešová, Simona
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /21./, Jablonec nad Nisou (CZ), 20220619
Year: 2023
Language: eng
Abstract: 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.
Keywords: Bayesian inversion; delayed-acceptance Metropolis-Hastings; Markov chain Monte Carlo; surrogate model
Project no.: TK02010118
Funding provider: GA TA ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar, ISBN 978-80-85823-73-8
Institution: Institute of Geonics AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: https://dml.cz/bitstream/handle/10338.dmlcz/703185/PANM_21-2022-1_6.pdf
Original record: https://hdl.handle.net/11104/0342777
Permalink: http://www.nusl.cz/ntk/nusl-524977
The record appears in these collections:
Research > Institutes ASCR > Institute of Geonics
Conference materials > Papers
Record created 2023-05-21, last modified 2024-04-15