Probabilistic numerics for PDE-constained inverse problems in MaxEnt
Jon Cockayne, Chris Oates, Mark Girolami and I have just had our paper “Probabilistic numerical methods for PDE-constrained Bayesian inverse problems” published in the Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. This paper complements our more extensive work “Probabilistic meshless methods for partial differential equations and Bayesian inverse problems” and gives a more concise presentation of the main ideas, aimed at a general audience.
J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Probabilistic numerical methods for PDE-constrained Bayesian inverse problems” in Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. G. Verdoolaege. AIP Conference Proceedings 1853:060001-1–060001-8, 2017.
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.
Published on Friday 9 June 2017 at 11:40 UTC #publication #prob-num #inverse-problems