A hybrid multiscale coarse-grained method for dynamics on complex networks

TL;DR

This paper introduces a hybrid multiscale coarse-grained method that efficiently simulates dynamics on large complex networks by combining detailed and coarse models, accurately capturing phase transitions while saving computational resources.

Contribution

The paper presents a novel hybrid multiscale coarse-grained approach that integrates microscopic and macroscopic simulations for network dynamics, improving efficiency and accuracy.

Findings

HMCG accurately reproduces phase transitions and critical phenomena.

HMCG significantly reduces computational cost compared to full microscopic simulations.

Method is general and applicable to various networked systems.

Abstract

Brute-force simulations for dynamics on very large networks are quite expensive. While phenomenological treatments may capture some macroscopic properties, they often ignore important microscopic details. Fortunately, one may be only interested in the property of local part and not in the whole network. Here, we propose a hybrid multiscale coarse-grained(HMCG) method which combines a fine Monte Carlo(MC) simulation on the part of nodes of interest with a more coarse Langevin dynamics on the rest part. We demonstrate the validity of our method by analyzing the equilibrium Ising model and the nonequilibrium susceptible-infected-susceptible model. It is found that HMCG not only works very well in reproducing the phase transitions and critical phenomena of the microscopic models, but also accelerates the evaluation of dynamics with significant computational savings compared to microscopic MC simulations directly for the whole networks. The proposed method is general and can be applied to a wide variety of networked systems just adopting appropriate microscopic simulation methods and coarse graining approaches.