Efficient dynamic importance sampling of rare events in one dimension - art. no. 016702

Exploiting stochastic path-integral theory, we obtain by simulation substan tial gains in efficiency for the computation of reaction rates in one-dimen sional, bistable, overdamped stochastic systems. Using a well-defined measu re of efficiency, we compare implementations of "dynamic importance samplin g" (DIMS) methods to unbiased simulation. The best DIMS algorithms are show n to increase efficiency by factors of approximately 20 for a 5k(B)T barrie r height and 300 for 9k(B)T, compared to unbiased simulation. The gains res ult from close emulation of natural (unbiased), instantonlike crossing even ts with artificially decreased waiting times between events that are correc ted for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event describe d 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-dimens ional models to larger systems, and suggest extensions to higher-dimensiona l systems.