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Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems

Zitieren Sie bitte immer diese URN: urn:nbn:de:0297-zib-59513
  • This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse problems while accounting, in a rigorous way, for the impact of the discretisation of the forward problem. In particular, this confers robustness to failure of meshless methods, with statistical inferences driven to be more conservative in the presence of significant solver error. In addition, (i) a principled learning-theoretic approach to minimise the impact of solver error is developed, and (ii) the challenging setting of inverse problems with a non-linear forward model is considered. The method is applied to parameter inference problems in which non-negligible solver error must be accounted for in order to draw valid statistical conclusions.

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Metadaten
Verfasserangaben:Jon Cockayne, Chris Oates, T. J. Sullivan, Mark Girolami
Dokumentart:ZIB-Report
Freies Schlagwort / Tag:Gaussian Processes; Inverse Problems; Meshless Methods; Partial Differential Equations; Probabilistic Numerics; Pseudo-Marginal MCMC
Datum der Erstveröffentlichung:25.05.2016
Schriftenreihe (Bandnummer):ZIB-Report (16-31)
ISSN:1438-0064
Preprint:urn:nbn:de:0297-zib-59513
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