Monte Carlo Sampling in Fractal Landscapes

Abstract

We propose a flat-histogram Monte Carlo method to efficiently sample fractal landscapes such as escape time functions of open chaotic systems. This is achieved by using a random-walk step which depends on the height of the landscape via the largest Lyapunov exponent of the associated chaotic system. By generalizing the Wang-Landau algorithm, we obtain a method which simultaneously constructs the density of states (escape time distribution) and the correct step-length distribution. As a result, averages are obtained in polynomial computational time, a dramatic improvement over the exponential scaling of traditional uniform sampling. Our results are not limited by the dimensionality of the phase space and are confirmed numerically for dimensions as large as 30.

5 pages, 5 figures; Published version

References in corpus (8)

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Cited by in corpus (8)

• Infinite densities for Lévy walks
• Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
• Efficiency of Monte Carlo Sampling in Chaotic Systems
• Importance Sampling of Rare Events in Chaotic Systems
• Searching chaotic saddles in high dimensions
• Taming chaos to sample rare events: the effect of weak chaos
• Monte Carlo sampling in diffusive dynamical systems
• Scale-invariance of ruggedness measures in fractal fitness landscapes