Article,
Analysis of the accelerated weighted ensemble methodology
Discrete and Continuous Dynamical Systems, (2013)
Abstract
The main issue addressed in this note is the study of an algorithm
to accelerate the computation of kinetic rates in the context of molecular dynamics
(MD). It is based on parallel simulations of short-time trajectories and
its main components are: a decomposition of phase space into macrostates or
cells, a resampling procedure that ensures that the number of parallel replicas
(MD simulations) in each macro-state remains constant, the use of multiple
populations (colored replicas) to compute multiple rates (e.g., forward and
backward rates) in one simulation. The method leads to enhancing the sampling
of macro-states associated to the transition states, since in traditional
MD these are likely to be depleted even after short-time simulations. By allowing
parallel replicas to carry different probabilistic weights, the number of
replicas within each macro-state can be maintained constant without introducing
any bias. The empirical variance of the estimated reaction rate, defined
as a probability flux, is expectedly diminished. This note is a first attempt
towards 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 having
been proposed in the literature within the past few years is discussed. Lastly,
numerical results are provided that illustrate the efficiency of the method.
