Cellular Probabilistic Automata - A Novel Method for Uncertainty Propagation

TL;DR

This paper introduces cellular probabilistic automata as a new density-based numerical method for uncertainty propagation in PDEs, demonstrating its effectiveness through water pipe contamination modeling.

Contribution

It presents a novel approach combining cellular automata theory with density discretization for uncertainty propagation in PDEs, with proven consistency and practical application.

Findings

Effective uncertainty propagation in PDEs demonstrated

Comparison shows advantages over Monte Carlo methods

Application to water pipe contamination modeling

Abstract

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.