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

Bold, Katherine A. and Rajendran, Karthikeyan and Ráth, Balázs and Kevrekidis, Ioannis G. (2014) An equation-free approach to coarse-graining the dynamics of networks. JOURNAL OF COMPUTATIONAL DYNAMICS, 1 (1). pp. 111-134. ISSN 2158-2491

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Abstract

We propose and illustrate an approach to coarse-graining the dynamics of evolving net- works (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 acceler- ate temporal simulations (through coarse projective integration), and to implement coarse- grained fixed point algorithms (through matrix-free Newton-Krylov GMRES). The approach is illustrated through a simple network evolution example, for which analytical approxima- tions 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.

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