Community integration algorithms (CIAs) for dynamical systems on networks

Dynamics of large-scale network processes underlies crucial phenomena ranging across all sciences. Forward simulation large models is often computationally prohibitive. Yet, most networks have intrinsic community structure. We exploit these communities and propose a fast algorithm for dynamics. In particular, aggregating the inputs node receives constitutes limiting factor in numerically simulating develop integration algorithms (CIAs) significantly reducing function-evaluations. obtain substantial reduction from polynomial to linear computational complexity. illustrate our results multiple applications including classical higher-order Kuramoto-type systems synchronisation Cucker–Smale exhibiting flocking behaviour on synthetic as well real-world networks. Numerical comparison theoretical analysis confirm robustness efficiency CIAs.