Accelerated dynamics: Mathematical foundations and algorithmic improvements

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.

References in corpus (2)

• A Generalized Parallel Replica Dynamics
• The parallel replica method for simulating long trajectories of Markov chains

Cited by in corpus (7)

• Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions
• Stochastic Resonance for Non-Equilibrium Systems
• gen.parRep: a first implementation of the Generalized Parallel Replica dynamics for the long time simulation of metastable biochemical systems
• Computing Long Timescale Biomolecular Dynamics using Quasi-Stationary Distribution Kinetic Monte Carlo (QSD-KMC)
• Statistical Estimation of the Poincar{é} constant and Application to Sampling Multimodal Distributions
• Perturbation theory for killed Markov processes and quasi-stationary distributions
• Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs