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Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

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Title: Probabilistic numerical methods for PDE-constrained Bayesian inverse problems
Authors: Cockayne, J
Oates, C
Sullivan, T
Girolami, M
Item Type: Conference 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.
Editors: Verdoolaege, G
Issue Date: 9-Jun-2017
Date of Acceptance: 1-Jun-2017
URI: http://hdl.handle.net/10044/1/66123
DOI: https://dx.doi.org/10.1063/1.4985359
ISBN: 9780735415270
ISSN: 1551-7616
Publisher: AIP Publishing
Journal / Book Title: AIP Conference Proceedings
Volume: 1853
Issue: 1
Copyright Statement: © 2017 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in AIP Conference Proceedings 2017 1853: 1 and may be found at https://dx.doi.org/10.1063/1.4985359
Conference Name: Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Keywords: Science & Technology
Physical Sciences
Physics, Applied
Physics, Multidisciplinary
Publication Status: Published
Start Date: 2016-07-10
Finish Date: 2016-07-15
Conference Place: Ghent Univ, Dept Appl Phys, Fus Data Sci Grp, Ghent, Belgium
Appears in Collections:Mathematics
Faculty of Natural Sciences