dorsal/arxiv
View SchemaEfficient Dynamic Importance Sampling of Rare Events in One Dimension
| Authors | Daniel M. Zuckerman, Thomas B. Woolf |
|---|---|
| Categories | |
| ArXiv ID | physics/0005073 |
| URL | https://arxiv.org/abs/physics/0005073 |
| DOI | 10.1103/PhysRevE.63.016702 |
Abstract
Exploiting stochastic path integral theory, we obtain \emph{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 $5 k_B T$ barrier height and 300 for $9 k_B T$, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instanton-like 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.
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"abstract": "Exploiting stochastic path integral theory, we obtain \\emph{by simulation}\nsubstantial gains in efficiency for the computation of reaction rates in\none-dimensional, bistable, overdamped stochastic systems. Using a well-defined\nmeasure of efficiency, we compare implementations of ``Dynamic Importance\nSampling\u0027\u0027 (DIMS) methods to unbiased simulation. The best DIMS algorithms are\nshown to increase efficiency by factors of approximately 20 for a $5 k_B T$\nbarrier height and 300 for $9 k_B T$, compared to unbiased simulation. The\ngains result from close emulation of natural (unbiased), instanton-like\ncrossing events with artificially decreased waiting times between events that\nare corrected for in rate calculations. The artificial crossing events are\ngenerated using the closed-form solution to the most probable crossing event\ndescribed by the Onsager-Machlup action. While the best biasing methods require\nthe second derivative of the potential (resulting from the ``Jacobian\u0027\u0027 term in\nthe action, which is discussed at length), algorithms employing solely the\nfirst derivative do nearly as well. We discuss the importance of\none-dimensional models to larger systems, and suggest extensions to\nhigher-dimensional systems.",
"arxiv_id": "physics/0005073",
"authors": [
"Daniel M. Zuckerman",
"Thomas B. Woolf"
],
"categories": [
"physics.comp-ph",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevE.63.016702",
"title": "Efficient Dynamic Importance Sampling of Rare Events in One Dimension",
"url": "https://arxiv.org/abs/physics/0005073"
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