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Efficiency of Monte Carlo sampling in chaotic systems.

Research paper by Jorge C JC Leitão, J M Viana Parente JM Lopes, Eduardo G EG Altmann

Indexed on: 11 Dec '14Published on: 11 Dec '14Published in: Physical review. E, Statistical, nonlinear, and soft matter physics



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 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.