The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins. The method is based on path factorization of the evolution operator and requires no prior knowledge of the underlying energy landscape. The efficiency of the new method is demonstrated in simulations of anomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetic trapping.Time evolution of many natural and engineering systems is described by a master equation (ME), i.e. a set of ordinary differential equations for the time-dependent vector of state probabilities [1,2]. For models with large (or infinite but countable) number of states, direct solution of the ME is prohibitive and kinetic Monte Carlo (kMC) is used instead to simulate the time evolution by generating sequences of stochastic transitions from one state to the next [3][4][5]. Statistically equivalent to the (most often unknown) solution of the ME, kMC finds growing number of applications in natural and engineering sciences. However still wider applicability of kMC is severely limited by the notorious kinetic trapping where the stochastic trajectory repeatedly visits a subset of states, a trapping basin, connected to each other by high-rate transitions while transitions out of the trapping basin are infrequent and take great many kMC steps to observe.In this Letter, we present an efficient method for sampling stochastic trajectories escaping from the trapping basins. Unlike recent methods that focus on short portions of the full kinetic path directly leading to the escapes and/or require equilibration over a path ensemble [6][7][8][9][10][11][12], our method constructs an entire stochastic trajectory within the trapping basin including the typically large numbers of repeated visits to each trapping state as well as the eventual escape. Referred hereafter as kinetic Path Sampling (kPS), the new algorithm is statistically equivalent to the standard kMC simulation and entails (i) iterative factorization of paths inside a trapping basin, (ii) sampling a single exit state within the basin's perimeter and (iii) generating a first-passage path and an exit time to the selected perimeter state through an exact randomization procedure. We demonstrate the accuracy and efficiency of kPS on two models: (1) diffusion on a random energy landscape specifically designed to yield a wide and continuous spectrum of time scales and (2) kinetics of phase separation in super-saturated solid solutions of copper in iron. The proposed method is immune to kinetic trapping and performs well under simulation conditions where the standard kMC simulations slows down to a crawl. In particular, it reaches later stages of phase separation in the Fe-Cu system and captures a qualitatively new kinetics and mechanism of copper precipitat...
Reaction paths and probabilities are inferred, in a usual Monte Carlo or molecular dynamic simulation, directly from the evolution of the positions of the particles. The process becomes time-consuming in many interesting cases in which the transition probabilities are small. A radically different approach consists of setting up a computation scheme where the object whose time evolution is simulated is the transition current itself. The relevant timescale for such a computation is the one needed for the transition probability rate to reach a stationary level, and this is usually substantially shorter than the passage time of an individual system. As an example, we show, in the context of the "benchmark" case of 38 particles interacting via the Lennard-Jones potential ("LJ(38)" cluster), how this method may be used to explore the reactions that take place between different phases, recovering efficiently known results, and uncovering new ones with small computational effort.
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