Efficiency of Monte Carlo sampling in chaotic systems
| Autor: | Eduardo G. Altmann, Jorge C. Leitão, João M. V. P. Lopes |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Mathematical optimization
Statistical Mechanics (cond-mat.stat-mech) Quantum Monte Carlo Monte Carlo method FOS: Physical sciences Markov chain Monte Carlo Computational Physics (physics.comp-ph) Nonlinear Sciences - Chaotic Dynamics 01 natural sciences 010305 fluids & plasmas Hybrid Monte Carlo symbols.namesake 0103 physical sciences symbols Dynamic Monte Carlo method Monte Carlo integration Monte Carlo method in statistical physics Statistical physics Chaotic Dynamics (nlin.CD) 010306 general physics Physics - Computational Physics Condensed Matter - Statistical Mechanics Monte Carlo molecular modeling Mathematics |
| Zdroj: | Physical review. E, Statistical, nonlinear, and soft matter physics. 90(5-1) |
| ISSN: | 1550-2376 |
| Popis: | In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on a flat-histogram simulation of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort of the simulation: (i) scales polynomially with the finite-time, a tremendous improvement over the exponential scaling obtained in usual uniform sampling simulations; and (ii) the polynomial scaling is sub-optimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal on the Monte Carlo procedure in chaotic systems. These results remain valid in other methods and show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations. 7 pages, 5 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|