Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

Cockayne, J; Oates, C; Sullivan, T; Girolami, M

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

Cockayne, J Oates, C

Sullivan, T Girolami, M

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Publication Type:: Conference Proceeding
Citation:: AIP Conference Proceedings, 2017, 1853
Issue Date:: 2017-06-09

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Field	Value	Language
dc.contributor.author	Cockayne, J	en_US
dc.contributor.author	Oates, C https://orcid.org/0000-0002-4444-8603	en_US
dc.contributor.author	Sullivan, T	en_US
dc.contributor.author	Girolami, M	en_US
dc.date.issued	2017-06-09	en_US
dc.identifier.citation	AIP Conference Proceedings, 2017, 1853	en_US
dc.identifier.isbn	9780735415270	en_US
dc.identifier.issn	0094-243X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/127439
dc.description.abstract	© 2017 Author(s). 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.	en_US
dc.relation.ispartof	AIP Conference Proceedings	en_US
dc.relation.isbasedon	10.1063/1.4985359	en_US
dc.title	Probabilistic numerical methods for PDE-constrained Bayesian inverse problems	en_US
dc.type	Conference Proceeding
utslib.citation.volume	1853	en_US
utslib.for	0804 Data Format	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US
pubs.volume	1853	en_US

Abstract:

© 2017 Author(s). 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.

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http://hdl.handle.net/10453/127439