标题： 基于伯努利概率测度空间的细胞自动机识别 显示英文标题

标题： Identification of Cellular Automata on Spaces of Bernoulli Probability Measures

摘要： 经典细胞自动机（CCAs）是一种强大的计算框架，用于通过局部相互作用对全局时空动态进行建模。 尽管CCAs已被应用于众多科学领域，但确定支配观察到的动态的局部规则仍然是一个具有挑战性的任务。 此外，确定性单元状态的潜在假设通常限制了CCAs在具有固有不确定性的系统中的适用性。 因此，本研究专注于概率测度空间上的细胞自动机（CAMs）的识别，其中单元状态由概率分布表示。 该框架能够对具有概率不确定性和空间变化动态的系统进行建模。 此外，我们将局部规则识别问题表述为参数估计问题，并提出一种基于自适应差分进化（SaDE）的元启发式搜索方法，以从观察数据中准确估计局部规则参数。 所提出的方法的有效性通过在具有不同邻域类型和半径的二维CAMs中的局部规则识别得到了验证。 显示英文摘要

摘要： 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.