Mathematical Analysis of Temperature Accelerated Dynamics

TL;DR

This paper provides a rigorous mathematical framework for temperature accelerated dynamics (TAD), enhancing its theoretical foundation and proposing modifications to improve its reliability in simulating metastable stochastic systems.

Contribution

It introduces a formal mathematical analysis of TAD using quasistationary distributions and proposes modifications to make the algorithm more rigorous.

Findings

Mathematically formalizes TAD using quasistationary distributions

Proposes modifications to improve TAD's rigor

Demonstrates the modified TAD in an idealized setting

Abstract

We give a mathematical framework for temperature accelerated dynamics (TAD), an algorithm proposed by M.R. S{\o}rensen and A.F. Voter to efficiently generate metastable stochastic dynamics. Using the notion of quasistationary distributions, we propose some modifications to TAD. Then considering the modified algorithm in an idealized setting, we show how TAD can be made mathematically rigorous.