TY - JOUR

T1 - A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)

AU - Lin, Ling

AU - Lu, Jianfeng

AU - Vanden-Eijnden, Eric

N1 - Funding Information:
In particular, for k D i , this is exactly what was to be shown. The proof is complete. □ Acknowledgment. The work of J.L. is partially supported by the National Science Foundation under grant DMS-1454939. The work of E.V.E. is partially supported by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation under grant DMR-1420073 and by the National Science Foundation under grant DMS-1522767.
Publisher Copyright:
© 2017 Wiley Periodicals, Inc.

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

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U2 - 10.1002/cpa.21725

DO - 10.1002/cpa.21725

M3 - Article

AN - SCOPUS:85019234701

VL - 71

SP - 1149

EP - 1177

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 6

ER -