Mathematical foundations of Accelerated Molecular Dynamics methods

TL;DR

This paper reviews recent mathematical analyses of Accelerated Dynamics algorithms, demonstrating their theoretical justification and potential for improved efficiency in modeling metastable state transitions.

Contribution

It provides a rigorous mathematical framework for understanding and validating Accelerated Dynamics methods using quasi-stationary distributions and Eyring-Kramers formulas.

Findings

Exit events can be modeled by kinetic Monte Carlo.

Under geometric assumptions, models can be parameterized with Eyring-Kramers formulas.

The analysis helps improve and generalize Accelerated Dynamics techniques.

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.