## Estimating exit rates in rare event dynamical systems via extrapolation

Please always quote using this URN: urn:nbn:de:0297-zib-56622

- In this article we present a new idea for approximating exit rates for diffusion processes living in a craggy landscape. We are especially interested in the exit rates of a process living in a metastable regions. Due to the fact that Monte Carlo simulations perform quite poor and are very computational expensive in this setting we create several similar situations with a smoothed potential. For this we introduce a new parameter $\lambda \in [0,1]$ ($\lambda = 1$ very smoothed potential, $\lambda=0$ original potential) into the potential which controls the influence the smoothing. We then sample the exit rate for different parameters $\lambda$ the exit rate from a given region. Due to the fact that $\lambda$ is connected to the exit rate we can use this dependency to approximate the real exit rate. The method can be seen as something between hyperdynamics and temperature accelerated MC.

Author: | Marcus Weber, Jannes Quer |
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Document Type: | ZIB-Report |

Tag: | rare event sampling, smoothing, membership functions, perturbed potential |

MSC-Classification: | 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) |

82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER | |

CCS-Classification: | G. Mathematics of Computing / G.3 PROBABILITY AND STATISTICS |

PACS-Classification: | 30.00.00 ATOMIC AND MOLECULAR PHYSICS / 31.00.00 Electronic structure of atoms and molecules: theory |

Date of first Publication: | 2015/11/26 |

Series (Serial Number): | ZIB-Report (15-54) |

ISSN: | 1438-0064 |