Probabilistic numerical methods for PDE-constrained Bayesian inverse problems
Probabilistic numerical methods for PDE-constrained Bayesian inverse problems
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.
Cockayne, Jonathan
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Oates, Chris J.
3af13c56-dc47-4d2c-867f-e4e933e74619
Sullivan, T.J.
1ef5be06-ad9c-44df-afdd-7b2294eb1e6b
Girolami, Mark
4feb7248-7beb-4edc-8509-139b4049d23b
9 June 2017
Cockayne, Jonathan
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Oates, Chris J.
3af13c56-dc47-4d2c-867f-e4e933e74619
Sullivan, T.J.
1ef5be06-ad9c-44df-afdd-7b2294eb1e6b
Girolami, Mark
4feb7248-7beb-4edc-8509-139b4049d23b
Cockayne, Jonathan, Oates, Chris J., Sullivan, T.J. and Girolami, Mark
(2017)
Probabilistic numerical methods for PDE-constrained Bayesian inverse problems.
36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering.
10 - 15 Jul 2016.
9 pp
.
(doi:10.1063/1.4985359).
Record type:
Conference or Workshop Item
(Paper)
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.
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Published date: 9 June 2017
Venue - Dates:
36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 2016-07-10 - 2016-07-15
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Local EPrints ID: 452770
URI: http://eprints.soton.ac.uk/id/eprint/452770
PURE UUID: 20460d24-5341-4ddf-9a36-5518d51d7f20
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Date deposited: 20 Dec 2021 17:33
Last modified: 17 Mar 2024 04:09
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Author:
Chris J. Oates
Author:
T.J. Sullivan
Author:
Mark Girolami
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