Cellular Probabilistic Automata - A Novel Method for Uncertainty Propagation

We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretizati...

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Bibliographic Details
Main Authors Kohler, Dominic, Müller, Johannes, Wever, Utz
Format Journal Article
LanguageEnglish
Published 05.02.2013
Subjects
Mathematics - Numerical Analysis
Mathematics - Probability
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Summary:We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method at the example of initial value uncertainties under deterministic dynamics and prove a consistency result. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations.
DOI:10.48550/arxiv.1302.1184