  The probabilistic cellular automaton (PCA) method is highlighted for its
relatively simple numerical algorithm and low computational cost in the
simulation of microstructural evolution. In this method, probabilistic state
change rules are implemented to compute the evolution of cell states at each
time step. The stochastic nature of this simulation method leads to
non-repeatable simulation results, introducing inherent uncertainty. In this
study, the uncertainty and dispersion in PCA simulations of microstructural
evolution were investigated. Hence, the probabilistic transformations of cell
states were meticulously considered at each time step, and discrete probability
distribution functions (dPDF) were introduced to analyze the frequency
distribution of simulation outcomes. To evaluate the performance of the
proposed dPDFs, cellular automaton models were developed with various numbers
of cells and distribution of transformation probabilities. Multiple iterations
of these simulations were conducted, and the validity of the presented
distribution functions was assessed through statistical analysis of the
simulations outcomes. Comparisons between PCA simulation results and
distribution functions demonstrate consistency, emphasizing the predictive
capability of the proposed models. Also, the effects of modeling parameters on
the uncertainty of simulation results in two and three-dimensional PCA modeling
were studied, introducing the coefficient of variation as a measure of
dispersion. Results indicate that increasing the number of boundary cells,
cellular resolution, and model size reduces uncertainty, enhancing the
repeatability of PCA simulation outcomes.
