Identification of Cellular Automata on Spaces of Bernoulli Probability Measures

TL;DR

This paper introduces a novel approach to identify cellular automata rules on probabilistic spaces, enabling modeling of systems with uncertainty, using a meta-heuristic search method for accurate parameter estimation from observed data.

Contribution

It extends classical cellular automata to probabilistic measures and proposes a Self-adaptive Differential Evolution method for local rule identification.

Findings

Effective rule identification demonstrated on 2D probabilistic automata

Applicable to various neighborhood types and radii

Improves modeling of uncertain systems

Abstract

Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that governs observed dynamics remains a challenging task. Moreover, the underlying assumption of deterministic cell states often limits the applicability of CCAs to systems characterized by inherent uncertainty. This study, therefore, focuses on the identification of Cellular Automata on spaces of probability measures (CAMs), where cell states are represented by probability distributions. This framework enables the modeling of systems with probabilistic uncertainty and spatially varying dynamics. Moreover, we formulate the local rule identification problem as a parameter estimation problem and propose a meta-heuristic search based on Self-adaptive Differential Evolution (SaDE) to estimate local rule parameters accurately from the observed data. The efficacy of the proposed approach is demonstrated through local rule identification in two-dimensional CAMs with varying neighborhood types and radii.