An Efficient Self-optimized Sampling Method for Rare Events in Nonequilibrium Systems

TL;DR

This paper introduces a self-optimized sampling method for rare events in nonequilibrium systems, improving efficiency and metastable state detection over traditional forward flux sampling by adaptively setting interfaces based on transition probabilities.

Contribution

The proposed method adaptively locates interfaces with equal transition probability, enhancing efficiency and metastable state identification in rare event sampling.

Findings

Significantly more efficient than conventional FFS.

Accurately reproduces two-step nucleation in Ising model.

Effectively detects intermediate metastable states.

Abstract

Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states. FFS usually suffers from two main difficulties: low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states. In the present work, we propose an approach to overcome these difficulties, by self-adaptively locating the interfaces on the fly in an optimized manner. Contrary to the conventional FFS which set the interfaces with euqal distance of the order parameter, our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition. This is done by firstly running long local trajectories starting from the current interface $\l_i$ to get the conditional probability distribution $P_c$, and then determining $\l_{i+1}$ by equalling $P_c$ to a give value $p_0$. With these optimized interfaces, FFS can be run in a much efficient way. In addition, our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that nither end at the initial state nor reach the next interface, the number of which will increase sharply from zero if such metastable states are encountered. We apply our approach to a model two-state system and a two-dimensional lattice gas Ising model. Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy, and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermidiate metastable state.