A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)

Ling Lin, Jianfeng Lu, Eric Vanden-Eijnden

Research output: Contribution to journalArticle

Abstract

Milestoning is a computational procedure that reduces the dynamics of complex systems to memoryless jumps between intermediates, or milestones, and only retains some information about the probability of these jumps and the time lags between them. Here we analyze a variant of this procedure, termed optimal milestoning, which relies on a specific choice of milestones to capture exactly some kinetic features of the original dynamical system. In particular, we prove that optimal milestoning permits the exact calculation of the mean first passage times (MFPT) between any two milestones. In so doing, we also analyze another variant of the method, called exact milestoning, which also permits the exact calculation of certain MFPTs, but at the price of retaining more information about the original system's dynamics. Finally, we discuss importance sampling strategies based on optimal and exact milestoning that can be used to bypass the simulation of the original system when estimating the statistical quantities used in these methods.

Original languageEnglish (US)
Pages (from-to)1149-1177
Number of pages29
JournalCommunications on Pure and Applied Mathematics
Volume71
Issue number6
DOIs
StatePublished - Jun 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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