Accelerated dynamics: Mathematical foundations and algorithmic improvements

TL;DR

This paper reviews recent mathematical and algorithmic advances for efficiently simulating long trajectories of metastable processes, with applications in materials science, based on quasi-stationary distributions.

Contribution

It provides a comprehensive review of mathematical foundations and algorithmic improvements for accelerated dynamics methods used in metastable process simulations.

Findings

Algorithms effectively generate long metastable trajectories

Mathematical analysis based on quasi-stationary distributions

Successful applications in materials science

Abstract

We present a review of recent works on the mathematical analysis of algorithms which have been proposed by A.F. Voter and co-workers in the late nineties in order to efficiently generate long trajectories of metastable processes. These techniques have been successfully applied in many contexts, in particular in the field of materials science. The mathematical analysis we propose relies on the notion of quasi stationary distribution.