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Kohler, D.* ; Marzouk, Y.M.* ; Müller, J. ; Wever, U.*

A new network approach to Bayesian inference in partial differential equations.

Int. J. Numer. Methods Eng. 104, 313-329 (2015)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state-discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen-Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Boyen-koller Algorithm ; Cellular Probabilistic Automata ; Dynamic Bayesian Networks ; Hyperbolic ; Inverse ; Partial Differential Equations ; Probabilistic Methods
ISSN (print) / ISBN 0029-5981
e-ISSN 1097-0207
Quellenangaben Volume: 104, Issue: 5, Pages: 313-329 Article Number: , Supplement: ,
Publisher Wiley
Publishing Place Chichester [u.a.]
Reviewing status Peer reviewed