Identification of Cellular Automata on Spaces of Bernoulli Probability Measures

2025-06-28

AI Summary

Conventional cellular automata (CCA) struggle to model complex systems characterized by intrinsic stochasticity and spatial heterogeneity. Method: This paper proposes cellular automata on probability measure spaces (CAM), where cell states are represented by Bernoulli probability measures. Crucially, local rule identification is reformulated as a parameter estimation problem in the probability measure space—departing from deterministic modeling paradigms. We design a metaheuristic optimization framework based on self-adaptive differential evolution (SaDE), jointly optimizing variable neighborhood structures and radii to infer rule parameters from observational data. Contribution/Results: Extensive validation on two-dimensional CAM demonstrates high-accuracy rule identification across diverse neighborhood configurations. The approach proves effective, robust, and generalizable for modeling uncertain systems, offering a principled probabilistic alternative to classical CCA.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Identify local rules governing probabilistic cellular automata dynamics
• Model systems with uncertainty using probability measure spaces
• Estimate local rule parameters via meta-heuristic search algorithms

Innovation

• Cellular Automata on probability measures spaces
• Parameter estimation via meta-heuristic search
• Self-adaptive Differential Evolution for rule identification