An equation-free approach to coarse-graining the dynamics of networks

TL;DR

This paper introduces an equation-free method for simplifying the analysis of evolving networks by combining short detailed simulations with coarse observables, enabling faster simulations and fixed point computations.

Contribution

It presents a novel equation-free framework for coarse-graining network dynamics, including acceleration of simulations and fixed point algorithms, validated on a simple network evolution example.

Findings

Validated the approach with analytical comparisons

Demonstrated acceleration of network simulations

Discussed criteria for selecting coarse observables

Abstract

We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-free framework: short bursts of detailed network evolution simulations are coupled with lifting and restriction operators that translate between actual network realizations and their (appropriately chosen) coarse observables. This framework is used here to accelerate temporal simulations (through coarse projective integration), and to implement coarsegrained fixed point algorithms (through matrix-free Newton-Krylov GMRES). The approach is illustrated through a simple network evolution example, for which analytical approximations to the coarse-grained dynamics can be independently obtained, so as to validate the computational results. The scope and applicability of the approach, as well as the issue of selection of good coarse observables are discussed.