Efficient integration of short-range models on complex networks

Complex, hierarchical or random network topolgies can give rise to unique behavior in many physical models. We study dynamical synchronization behavior in Kuramoto models on power grids and brain connectomes with millons of connections and O(100k) nodes. At these scales it is crucial to use the sparsity when computing derivatives, which, due to the random network structure, makes employing modern parallel hardware tricky. Here, we present our approach to numerically solving large systems ordinary differential equations on random directed graphs, where we focus on the computationally expensive task of computing derivatives and leave the common integration step to the boost::odeint library. Our application can utilize both parallel CPUs and GPUs. We also provide an overview of our results on human and fly brain connectomes as well as failure cascades in power grids and provide a measure of the advantage gained from our computational optimization efforts.