Importance sampling of rare events in chaotic systems

Leitão, Jorge C.; Viana Parente Lopes, Joao M.; Altmann, Eduardo G.

doi:10.1140/epjb/e2017-80054-3

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Importance sampling of rare events in chaotic systems

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Leitão, Jorge C.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Altmann, Eduardo G.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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https://link.springer.com/article/10.1140%2Fepjb%2Fe2017-80054-3
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Citation

Leitão, J. C., Viana Parente Lopes, J. M., & Altmann, E. G. (2017). Importance sampling of rare events in chaotic systems. European Physical Journal B, 90(10): 181. doi:10.1140/epjb/e2017-80054-3.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002E-801B-2

Abstract

Finding and sampling rare trajectories in dynamical systems is a difficult computational task underlying numerous problems and applications. In this paper we show how to construct MetropolisHastings Monte-Carlo methods that can efficiently sample rare trajectories in the (extremely rough) phase space of chaotic systems. As examples of our general framework we compute the distribution of finite-time Lyapunov exponents (in different chaotic maps) and the distribution of escape times (in transient-chaos problems). Our methods sample exponentially rare states in polynomial number of samples (in both low-and high-dimensional systems).