The use of radial basis function surrogate models for sampling process acceleration in Bayesian inversio

0537236 - ÚGN 2021 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Domesová, Simona
The use of radial basis function surrogate models for sampling process acceleration in Bayesian inversio.
Lecture Notes in Electrical Engineering. Vol. 554. Cham: Springer Nature Switzerland AG, 2020 - (Zelinka, I.; Brandstetter, P.; Trong Dao, T.; Hoang Duy, V.; Kim, S.), s. 228-238. ISBN 978-3-030-14906-2. ISSN 1876-1100. E-ISSN 1876-1119.
[International Conference on Advanced Engineering Theory and Applications 2018 /5./. Ostrava (CZ), 11.11.2018-13.11.2018]
Grant CEP: GA MŠMT LQ1602
Institucionální podpora: RVO:68145535
Klíčová slova: Bayesian inversion * Metropolis-Hastings * radial basis functions * surrogate model * uncertainty quantification
Obor OECD: Applied mathematics
https://link.springer.com/chapter/10.1007%2F978-3-030-14907-9_23

The Bayesian approach provides a natural way of solving engineering inverse problems including uncertainties. The objective is to describe unknown parameters of a mathematical model based on noisy measurements. Using the Bayesian approach, the vector of unknown parameters is described by its joint probability distribution, i.e. the posterior distribution. To provide samples, Markov Chain Monte Carlo methods can be used. Their disadvantage lies in the need of repeated evaluations of the mathematical model that are computationally expensive in the case of practical problems.

This paper focuses on the reduction of the number of these evaluations. Specifically, it explores possibilities of the use of radial basis function surrogate models in sampling methods based on the Metropolis-Hastings algorithm. Furthermore, updates of the surrogate model during the sampling process are suggested. The procedure of surrogate model updates and its integration into the sampling algorithm is implemented and supported by numerical experiments.
Trvalý link: http://hdl.handle.net/11104/0314976