Probabilistic numerical methods for PDE-constrained Bayesian inverse problems
File(s)1.4985359(1).pdf (1.37 MB)
Published version
Author(s)
Cockayne, Jon
Oates, Chris
Sullivan, Tim
Girolami, Mark
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.
Editor(s)
Verdoolaege, G
Date Issued
2017-06-09
Date Acceptance
2017-06-01
Citation
AIP Conference Proceedings, 2017, 1853 (1)
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
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000410164000011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Source
Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Subjects
Science & Technology
Physical Sciences
Physics, Applied
Physics, Multidisciplinary
Physics
PARTIAL-DIFFERENTIAL-EQUATIONS
Publication Status
Published
Start Date
2016-07-10
Finish Date
2016-07-15
Coverage Spatial
Ghent Univ, Dept Appl Phys, Fus Data Sci Grp, Ghent, Belgium