Monte Carlo Sampling in Fractal Landscapes

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Jorge C Leitao (Author) Other; Viana Parente Lopes, JMVP (Author) FEUP; Eduardo G Altmann (Author) Other

Journal

Title: Physical Review Letters

Vol. 110

ISSN: 0031-9007

Publisher: American Physical Society

Indexing

ISI Web of Knowledge - 10 Citations

Scopus - 9 Citations

Scientific classification

FOS: Natural sciences > Physical sciences

Other information

Authenticus ID: P-005-0MX

DOI: 10.1103/physrevlett.110.220601

Abstract (EN): We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 5