We propose a novel density based numerical method for uncertainty propagationunder certain partial differential equation dynamics. The main idea is totranslate them into objects that we call cellular probabilistic automata and toevolve the latter. The translation is achieved by state discretization as inset oriented numerics and the use of the locality concept from cellularautomata theory. We develop the method at the example of initial valueuncertainties under deterministic dynamics and prove a consistency result. Asan application we discuss arsenate transportation and adsorption in drinkingwater pipes and compare our results to Monte Carlo computations.
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