Stochastic modeling of deterministic laser chaos using generator extended dynamic mode decomposition

TL;DR

This paper demonstrates how stochastic models derived from deterministic laser chaos using Koopman operator techniques can effectively capture essential dynamics and improve reinforcement learning applications.

Contribution

It introduces a novel approach to model laser chaos with stochastic processes derived from deterministic data via generator extended dynamic mode decomposition.

Findings

Stochastic models recover key features of laser chaos.

Low-pass filtered data suffices for accurate modeling.

Models enhance reinforcement learning performance.

Abstract

Recently, chaotic phenomena in laser dynamics have attracted much attention to its applied aspects, and a synchronization phenomenon, leader-laggard relationship, in time-delay coupled lasers has been used in reinforcement learning. In the present paper, we discuss the possibility of capturing the essential stochasticity of the leader-laggard relationship; in nonlinear science, it is known that coarse-graining allows one to derive stochastic models from deterministic systems. We derive stochastic models with the aid of the Koopman operator approach, and we clarify that the low-pass filtered data is enough to recover the essential features of the original deterministic chaos, such as peak shifts in the distribution of being the leader and a power-law behavior in the distribution of switching-time intervals. We also confirm that the derived stochastic model works well in reinforcement learning tasks, i.e., multi-armed bandit problems, as with the original laser chaos system.