Monte Carlo Sampling in Fractal Landscapes

• Tipo: Artigo em Revista Científica Internacional
• Data: 2013

Autores

Jorge C Leitao (Autor) Outra; Viana Parente Lopes, JMVP (Autor) FEUP; Eduardo G Altmann (Autor) Outra

Revista

Título: Physical Review Letters

Vol. 110

ISSN: 0031-9007

Editora: American Physical Society

Indexação

ISI Web of Knowledge - 10 Citações

Scopus - 9 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Física

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 5