Event horizon kinetic Monte Carlo

Abstract

In this study, we present a novel approach for modeling the dynamics of stochastic processes. The fundamental concept involves constructing a stochastic Markov chain comprising states separated by more than one stochastic event. Initially, the method explores the network of neighboring states connected by stochastic events. This exploration results in a “horizon” of events leading to a set of “boundary” states at the periphery of each local network. Subsequently, the next member in the Markov chain is selected from the “boundary” states based on the probability of reaching each of the “boundary” states for the first time. Meanwhile, the simulation clock is updated according to the time required to reach the boundary for the first time. This can be achieved using an analytical approach, where the probability of reaching each boundary state for the first time is estimated using absorbing conditions for all boundary states in the analytical solution of a master equation describing the local network of states around each current state. The proposed method is demonstrated in modeling the dynamics in networks of stochastic reactions but can be easily applied in any stochastic system whose dynamics can be expressed via the solution of a master equation. It is expected to enhance the efficiency of event-driven Monte Carlo simulations, originally introduced by Gillespie and widely regarded as the gold standard in the field, especially in cases where the presence of events is characterized by different timescales.