Analysis of the Accelerated Weighted Ensemble methodology
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.