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Probabilistic numerical methods for PDE-constrained Bayesian inverse problems
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Cockayne, Jon, Oates, Chris J., Sullivan, T. J. and Girolami, Mark (2017) Probabilistic numerical methods for PDE-constrained Bayesian inverse problems. In: 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Ghent, Belgium, 10-15 Jul 2016. Published in: AIP Conference Proceedings, 1853 (1). doi:10.1063/1.4985359 ISSN 0094-243X.
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WRAP-Probabilistics-numerical-methods-PDE-constrained-Sullivan-2017.pdf - Accepted Version - Requires a PDF viewer. Download (1091Kb) | Preview |
Official URL: http://dx.doi.org/10.1063/1.4985359
Abstract
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.
| Item Type: | Conference Item (Paper) | |||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Probabilities, Bayesian statistical decision theory, Differential equations, Partial, Discretization (Mathematics) | |||||||||||||||||||||
| Journal or Publication Title: | AIP Conference Proceedings | |||||||||||||||||||||
| Publisher: | American Institute of Physics | |||||||||||||||||||||
| ISSN: | 0094-243X | |||||||||||||||||||||
| Official Date: | 9 June 2017 | |||||||||||||||||||||
| Dates: |
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| Volume: | 1853 | |||||||||||||||||||||
| Number: | 1 | |||||||||||||||||||||
| Article Number: | 060001 | |||||||||||||||||||||
| DOI: | 10.1063/1.4985359 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Reuse Statement (publisher, data, author rights): | โThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Cockayne, Jon, Oates, Chris, Sullivan, T. J. and Girolami, Mark (2017) Probabilistic numerical methods for PDE-constrained Bayesian inverse problems. In: Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. Published in: AIP Conference Proceedings, 1853 (1). doi:10.1063/1.4985359 and may be found at http://dx.doi.org/10.1063/1.4985359 | |||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
| Date of first compliant deposit: | 10 April 2020 | |||||||||||||||||||||
| Date of first compliant Open Access: | 15 April 2020 | |||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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| Conference Paper Type: | Paper | |||||||||||||||||||||
| Title of Event: | 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering | |||||||||||||||||||||
| Type of Event: | Conference | |||||||||||||||||||||
| Location of Event: | Ghent, Belgium | |||||||||||||||||||||
| Date(s) of Event: | 10-15 Jul 2016 |
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