Efficiency of Monte Carlo Sampling in Chaotic Systems
arXiv:1407.5343 · doi:10.1103/PhysRevE.90.052916
Abstract
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on a flat-histogram simulation of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort of the simulation: (i) scales polynomially with the finite-time, a tremendous improvement over the exponential scaling obtained in usual uniform sampling simulations; and (ii) the polynomial scaling is sub-optimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal on the Monte Carlo procedure in chaotic systems. These results remain valid in other methods and show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.
arXiv comment7 pages, 5 figures
References in corpus (14)
- An efficient, multiple range random walk algorithm to calculate the density of states
- Optimized parallel tempering simulations of proteins
- Probing rare physical trajectories with Lyapunov weighted dynamics
- Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
- Characteristic distributions of finite-time Lyapunov exponents
- Large deviations of Lyapunov exponents
- Precision shooting: Sampling long transition pathways
- Fluctuations of finite-time stability exponents in the standard map and the detection of small islands
- Instability statistics and mixing rates
- Identifying rare chaotic and regular trajectories in dynamical systems with Lyapunov weighted path sampling
- Optimized multicanonical simulations: a new proposal based on classical fluctuation theory
- Monte Carlo Sampling in Fractal Landscapes
- Analytical study of tunneling times in flat histogram Monte Carlo
- Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems
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- Data-driven prediction and prevention of extreme events in a spatially extended excitable system
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- Searching chaotic saddles in high dimensions
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- Remarkable similarities in distributions of dynamical observables in chaotic systems