A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/14044Collections
More Info
Show full item recordScholars@Duke
Jianfeng Lu
Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm
development for problems from computational physics, theoretical chemistry, materials
science and other related fields.More specifically, his current research focuses include:Electronic
structure and many body problems; quantum molecular dynamics; multiscale modeling
and analysis; rare events and sampling techniques.

Articles written by Duke faculty are made available through the campus open access policy. For more information see: Duke Open Access Policy
Rights for Collection: Scholarly Articles
Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info