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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

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Author:Jon Cockayne, Chris Oates, T. J. Sullivan, Mark Girolami
Document Type:In Proceedings
Parent Title (English):Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
First Page:060001-1
Last Page:060001-8
Series:AIP Conference Proceedings
Year of first publication:2017
ArXiv Id:http://arxiv.org/abs/1701.04006