Mathematical Foundations of Accelerated Molecular Dynamics Methods
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The objective of this review chapter 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.
This work is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement number 614492. Part of this work was completed during the long programs “Large deviation theory in statistical physics: Recent advances and future challenges” at the International Centre for Theoretical Sciences (Bangalore) and “Complex High-Dimensional Energy Landscapes” at the Institute for Pure and Applied Mathematics (UCLA). The author would like to thank ICTS and IPAM for their hospitality.
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