Population dynamics method with a multi-canonical feedback control

TL;DR

This paper improves the population dynamics method for large deviation calculations in Markov processes by introducing control forces via an iterative feedback scheme, reducing systematic errors especially in complex or weak-noise systems.

Contribution

The paper presents a novel control force approach with an iterative feedback scheme to mitigate systematic errors in population dynamics methods.

Findings

Significantly reduced errors in simple models.

Enhanced accuracy near dynamical phase transitions.

Potential for application to complex systems.

Abstract

We discuss the Giardin\`a-Kurchan-Peliti population dynamics method for evaluating large deviations of time averaged quantities in Markov processes [Phys. Rev. Lett. \textbf{96}, 120603 (2006)]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dynamical phase transitions. We show how these errors can be mitigated by introducing control forces within the algorithm. These forces are determined by an iteration-and-feedback scheme, inspired by multicanonical methods in equilibrium sampling. We demonstrate substantially improved results in a simple model and we discuss potential applications to more complex systems.