Mathematical foundations of Accelerated Molecular Dynamics methods

Tony Lelièvre 1, 2
2 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : The objective of this review article is to present recent results on the mathematical analysis of the Accelerated Dynamics algorithms introduced by A.F. Voter in collaboration with D. Perez and M. Sorensen. Using the notion of quasi-stationary distribution, one is able to rigorously justify the fact that the exit event from a metastable state for the Langevin or overdamped Langevin dynamics can be modeled by a kinetic Monte Carlo model. Moreover, under some geometric assumptions, one can prove that this kinetic Monte Carlo model can be parameterized using Eyring-Kramers formulas. These are the building blocks required to analyze the Accelerated Dynamics algorithms, to understand their efficiency and their accuracy, and to improve and generalize these techniques beyond their original scope.
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https://hal.archives-ouvertes.fr/hal-01686062
Contributor : Tony Lelièvre <>
Submitted on : Wednesday, January 17, 2018 - 8:01:33 AM
Last modification on : Friday, April 19, 2019 - 4:55:20 PM

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  • HAL Id : hal-01686062, version 1
  • ARXIV : 1801.05347

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Tony Lelièvre. Mathematical foundations of Accelerated Molecular Dynamics methods. 2018. ⟨hal-01686062⟩

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