Efficiency of Monte Carlo sampling in chaotic systems

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Leitao, JC (Author) Other; Viana Parente Lopes, JMVP (Author) FCUP; Altmann, EG (Author) Other

Journal

Title: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Vol. 90

ISSN: 1539-3755

Publisher: American Physical Society

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 7 Citations

Other information

Authenticus ID: P-00A-007

DOI: 10.1103/physreve.90.052916

Abstract (EN): In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 7