Cellular probabilistic automata—a novel method for uncertainty propagation

Dominic Kohler, Johannes Müller, Utz Wever

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We propose a novel density based numerical method for uncertainty propagation under distinct 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 using the example of initial value uncertainties under deterministic dynamics and show that it is consistent. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations.

Original languageEnglish
Pages (from-to)29-54
Number of pages26
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume2
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Cellular automata
  • Set oriented numerics
  • Uncertainty propagation for partial differential equations

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