Sensitivity analysis of colored noise-driven interacting particle systems

TL;DR

This paper introduces an efficient sensitivity analysis method for colored noise-driven interacting particle systems, extending existing techniques to account for noise spectrum effects and applying it to systems with Coulomb interactions.

Contribution

The paper develops a sensitivity analysis method based on unperturbed simulations that accounts for noise spectrum effects, extending previous Malliavin weight sampling approaches.

Findings

Sensitivity index depends on noise variance, correlation time, and spectrum.

Exact formulas derived for linear response in harmonic potential.

System dynamics are influenced by the noise spectrum in complex ways.

Abstract

We propose an efficient sensitivity analysis method for a wide class of colored noise-driven interacting particle systems (IPS). Our method is based on unperturbed simulations and significantly extends the Malliavin weight sampling method proposed by Szamel (EPL, 117 (2017) 50010) for evaluating sensitivities such as linear response functions of IPS driven by simple Ornstein-Uhlenbeck processes. We show that the sensitivity index depends not only on two effective parameters that characterize the variance and correlation time of the noise, but also on the noise spectrum. In the case of a single particle in a harmonic potential, we obtain exact analytical formulas for two types of linear response functions. By applying our method to a system of many particles interacting via a repulsive screened Coulomb potential, we compute the mobility and effective temperature of the system. Our results show that the system dynamics depend, in a nontrivial way, on the noise spectrum.