Importance sampling of rare events in chaotic systems

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

*Corresponding author for this work

Research output: Contribution to journalReviewResearchpeer-review

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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,].

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

Bibliographical note

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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