[SY-N6] Strategies for optimal construction of Markov chain representations of atomistic dynamics
A common way of representing the long-time dynamics of materials is in terms of a Markov chain that specifies the transition rates for transitions between metastable states. This chain can either be used to generate trajectories using kinetic Monte Carlo, or analyzed directly, e.g., in terms of first passage times between distant states. While a number of approaches have been proposed to infer such a representation from direct molecular dynamics (MD) simulations, challenges remain. For example, as chains inferred from a finite amount of MD will in general be incomplete, quantifying their completeness is extremely desirable. In addition, making the construction of the chain as computationally affordable as possible is paramount. In this work, we simultaneously address these two questions. We first quantify the local completeness of the chain in terms of Bayesian estimators of the yet-unobserved rate, and its global completeness in terms of the residence time of trajectories within the explored subspace. We then systematically reduce the cost of creating the chain by maximizing the increase in residence time against the distribution of states in which additional MD is carried out and the temperature at which these are respectively carried out. Using as example the behavior of vacancy and interstitial clusters in materials, we demonstrate that this is an efficient, fully automated, and massively-parallel scheme to efficiently explore the long-time behavior of materials.