Probabilistic cellular automata simulation of microstructure evolution: the role of model parameters on precision and uncertainty

Abstract Probabilistic cellular automata (PCA) is a widely used and cost-efficient method for simulating microstructural evolution. In this method, probabilistic state change rules determine the evolution of cell states at each time step. However, its stochastic nature introduces inherent uncertainty, leading to non-repeatable results. Most microstructural simulation studies assess the accuracy of simulations by comparing predicted results with experimental observations, neglecting uncertainties in mathematical models and algorithms. In this study, the precision and stochastic behavior of microstructure evolution in the PCA simulations were investigated. The probabilities of transformations of cell states at each time step were formulated, and discrete probability distribution functions (dPDF) were introduced to analyze the frequency distribution of simulation outcomes. The performance and consistency of these dPDFs were assessed by comparing statistical analyzes of PCA simulation results with dPDF predictions, revealing that the variance of simulation results is less than that of the binomial distribution function. Additionally, the effects of modeling parameters, such as model size, cellular resolution, and probability distribution of state changes in two- and three-dimensional PCA modeling, on the precision and reliability of simulation results were studied. In PCA models, simulation uncertainty inversely relates to the square root of model size. Furthermore, in 2D simulations, uncertainty is inversely proportional to the square root of the cellular resolution, while in 3D simulations, it is inversely proportional to the cellular resolution itself. These findings provide a simple and computationally efficient method for evaluating PCA simulation uncertainty and determining optimal simulation parameters, including model size, cellular resolution, and dimensionality.