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Importance sampling of rare events in chaotic systems

Author

Listed:
  • Jorge C. Leitão

    (Max Planck Institute for the Physics of Complex Systems
    DTU Compute, Technical University of Denmark)

  • João M. Viana Parente Lopes

    (University of Minho
    Physics Engineering Department, Engineering Faculty of the University of Porto)

  • Eduardo G. Altmann

    (Max Planck Institute for the Physics of Complex Systems
    School of Mathematics and Statistics, University of Sydney)

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 ].

Suggested Citation

  • Jorge C. Leitão & João M. Viana Parente Lopes & Eduardo G. Altmann, 2017. "Importance sampling of rare events in chaotic systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(10), pages 1-23, October.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:10:d:10.1140_epjb_e2017-80054-3
    DOI: 10.1140/epjb/e2017-80054-3
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    Statistical and Nonlinear Physics;

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