Monte Carlo sampling in diffusive dynamical systems

TL;DR

This paper presents a Monte Carlo algorithm that improves the efficiency of computing transport properties in chaotic dynamical systems by focusing on significant trajectories using importance sampling and a Markov chain approach.

Contribution

The authors introduce a novel Monte Carlo method utilizing importance sampling and a correlated proposal to enhance the computation of transport properties in chaotic systems.

Findings

Outperforms direct sampling methods

Outperforms alternative Metropolis-Hastings proposals

Validated on 1D and 2D chaotic systems

Abstract

We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements, where deviations from a diffusive process are most prominent. We search for initial conditions using a proposal that correlates states in the Markov chain constructed via a Metropolis-Hastings algorithm. We show that our method outperforms the direct sampling method and also Metropolis-Hastings methods with alternative proposals. We test our general method through numerical simulations in 1D (box-map) and 2D (Lorentz gas) systems.