Reliable kinetic Monte Carlo simulation based on random set sampling

Kinetic Monte Carlo (KMC) method has been widely used in simulating rare events such as chemical reactions or phase transitions. Yet lack of complete knowledge of transitions and the associated rates is one major challenge for accurate KMC predictions. In this paper, a reliable KMC (R-KMC) mechanism is proposed in which sampling is based on random sets instead of random numbers to improve the robustness of KMC results. In R-KMC, rates or propensities are interval estimates instead of precise numbers. A multi-event algorithm based on generalized interval probability is developed. The weak convergence of the multi-event algorithm towards the traditional KMC is demonstrated with a generalized Chapman–Kolmogorov equation.