Analysis of the Accelerated Weighted Ensemble methodology

Authors: 
Ronan Costaouec, Haoyun Feng, Jesus A. Izaguirre, Eric Darve
Citation: 
DYNAMICAL SYSTEMS (2013): 171-181.
Publication Date: 
November, 2013

The main issue addressed in this note is the study of an algorithmto accelerate the computation of kinetic rates in the context of molecular dy-namics (MD). It is based on parallel simulations of short-time trajectories andits main components are: a decomposition of phase space into macrostates orcells, a resampling procedure that ensures that the number of parallel replicas(MD simulations) in each macro-state remains constant, the use of multiplepopulations (colored replicas) to compute multiple rates (e.g., forward andbackward rates) in one simulation. The method leads to enhancing the sam-pling of macro-states associated to the transition states, since in traditionalMD these are likely to be depleted even after short-time simulations. By al-lowing parallel replicas to carry different probabilistic weights, the number ofreplicas within each macro-state can be maintained constant without introduc-ing any bias. The empirical variance of the estimated reaction rate, definedas a probability flux, is expectedly diminished. This note is a first attempttowards a better mathematical and numerical understanding of this method.It provides first a mathematical formalization of the notion of colors. Then,the link between this algorithm and a set of closely related methods havingbeen proposed in the literature within the past few years is discussed. Lastly,numerical results are provided that illustrate the efficiency of the method.