Uncertainty Assessment of Probabilistic Cellular Automata Simulations in Microstructure Evolution

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.