Manzoni, A., Pagani, S. and Lassila, T. (2016) Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models. SIAM/ASA Journal on Uncertainty Quantification, 4 (1). pp. 380-412. ISSN 2166-2525
Abstract
Computational inverse problems related to partial differential equations (PDEs) often contain nuisance parameters that cannot be effectively identified but still need to be considered as part of the problem. The objective of this work is to show how to take advantage of a reduced order framework to speed up Bayesian inversion on the identifiable parameters of the system, while marginalizing away the (potentially large number of) nuisance parameters. The key ingredients are twofold. On the one hand, we rely on a reduced basis (RB) method, equipped with computable a posteriori error bounds, to speed up the solution of the forward problem. On the other hand, we develop suitable reduction error models (REMs) to quantify in an inexpensive way the error between the full-order and the reduced-order approximation of the forward problem, in order to gauge the effect of this error on the posterior distribution of the identifiable parameters. Numerical results dealing with inverse problems governed by elliptic PDEs in the case of both scalar parameters and parametric fields highlight the combined role played by RB accuracy and REM effectivity.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Society for Industrial and Applied Mathematics This is an author produced version of a paper subsequently published in SIAM/ASA Journal on Uncertainty Quantification. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Electronic and Electrical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Mar 2016 13:38 |
Last Modified: | 04 May 2016 03:41 |
Published Version: | http://dx.doi.org/10.1137/140995817 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Refereed: | Yes |
Identification Number: | 10.1137/140995817 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:95248 |