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].
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Leitão, J.C., Parente Lopes, J.M.V. & Altmann, E.G. Importance sampling of rare events in chaotic systems. Eur. Phys. J. B 90, 181 (2017). https://doi.org/10.1140/epjb/e2017-80054-3
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DOI: https://doi.org/10.1140/epjb/e2017-80054-3