Importance sampling of rare events in chaotic systems

Jorge C. Leitão, João M. Viana Parente Lopes and Eduardo G. Altmann ()
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Jorge C. Leitão: Max Planck Institute for the Physics of Complex Systems
João M. Viana Parente Lopes: University of Minho
Eduardo G. Altmann: Max Planck Institute for the Physics of Complex Systems

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 10, 1-23

Abstract: 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 ].

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1140/epjb/e2017-80054-3

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