Parameter estimation for cellular automata

TL;DR

This paper presents a robust statistical method for estimating parameters in cellular automata models, focusing on discrete rules and patterns, which significantly influence the resulting structures in complex systems.

Contribution

It introduces a novel Gaussian likelihood-based approach for parameter estimation in discrete cellular automata, improving accuracy and robustness over previous methods.

Findings

Method effectively estimates parameters for cellular automata

Approach is robust across different domain sizes and iterations

Applicable to various pattern characteristics

Abstract

Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and successfully apply a sound statistical method to estimate these parameters. The decisive difference to earlier applications of such approaches is that, in our case, both the CA rules and the resulting patterns are discrete. The method is based on constructing Gaussian likelihoods using characteristics of the structures, such as the mean particle size. We show that our approach is robust for the method parameters, domain size of patterns, or CA iterations.