Efficient dynamic importance sampling of rare events in one dimension

Daniel M. Zuckerman and Thomas B. Woolf
Phys. Rev. E 63, 016702 – Published 27 December 2000
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Abstract

Exploiting stochastic path-integral theory, we obtain by simulation substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of “dynamic importance sampling” (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a 5kBT barrier height and 300 for 9kBT, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instantonlike crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the “Jacobian” term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.

  • Received 25 May 2000

DOI:https://doi.org/10.1103/PhysRevE.63.016702

©2000 American Physical Society

Authors & Affiliations

Daniel M. Zuckerman1,* and Thomas B. Woolf1,2,†

  • 1Department of Physiology, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205
  • 2Department of Biophysics, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205

  • *Email address: dmz@groucho.med.jhmi.edu
  • Email address: woolf@groucho.med.jhmi.edu

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Vol. 63, Iss. 1 — January 2001

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