# American Institute of Mathematical Sciences

2013, 2013(special): 171-181. doi: 10.3934/proc.2013.2013.171

## Analysis of the accelerated weighted ensemble methodology

 1 Mechanical Engineering Department, Stanford University, CA, United States 2 Computer Science and Engineering, University of Notre Dame, IN, United States, United States 3 Mechanical Engineering Department and Institute for Computational and Mathematical Engineering, Stanford University, CA, United States

Received  September 2012 Revised  September 2013 Published  November 2013

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.
Citation: Ronan Costaouec, Haoyun Feng, Jesús Izaguirre, Eric Darve. Analysis of the accelerated weighted ensemble methodology. Conference Publications, 2013, 2013 (special) : 171-181. doi: 10.3934/proc.2013.2013.171
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