Importance sampling of rare events in chaotic systems

Jorge C. Leitão, João M.Viana Parente Lopes, Eduardo G. Altmann*

*Corresponding author for this work

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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 Metropolis-Hastings 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). An open-source software that implements our algorithms and reproduces our results can be found in reference [J. Leitao, A library to sample chaotic systems, 2017, https://github.com/jorgecarleitao/chaospp].

Original languageEnglish
Article number181
JournalEuropean Physical Journal B
Volume90
Issue number10
Number of pages23
ISSN1434-6028
DOIs
Publication statusPublished - 2017

Bibliographical note

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this

Leitão, Jorge C. ; Parente Lopes, João M.Viana ; Altmann, Eduardo G. / Importance sampling of rare events in chaotic systems. In: European Physical Journal B. 2017 ; Vol. 90, No. 10.
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Importance sampling of rare events in chaotic systems. / Leitão, Jorge C.; Parente Lopes, João M.Viana; Altmann, Eduardo G.

In: European Physical Journal B, Vol. 90, No. 10, 181, 2017.

Research output: Contribution to journalReviewResearchpeer-review

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AU - Parente Lopes, João M.Viana

AU - Altmann, Eduardo G.

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AB - 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 Metropolis-Hastings 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). An open-source software that implements our algorithms and reproduces our results can be found in reference [J. Leitao, A library to sample chaotic systems, 2017, https://github.com/jorgecarleitao/chaospp].

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