Efficient characterisation of large deviations using population dynamics

TL;DR

This paper analyzes the efficiency of population dynamics algorithms, specifically the cloning method, for studying large deviations in stochastic processes, highlighting convergence issues and optimization strategies.

Contribution

It provides a detailed investigation of the convergence behavior of the cloning algorithm for large deviations, especially near phase transitions, and offers optimization insights for parallel computing.

Findings

Convergence is challenging near dynamical phase transitions.

Optimization of algorithm parameters improves performance.

Parallel implementation enhances computational efficiency.

Abstract

We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. Using the simple symmetric exclusion process as a prototypical example, we investigate the convergence of the results with respect to the algorithmic parameters, focussing on the dynamical phase transition between homogeneous and inhomogeneous states, where convergence is relatively difficult to achieve. We discuss how the performance of the algorithm can be optimised, and how it can be efficiently exploited on parallel computing platforms.