  We consider the problem of optimizing the interconnection graphs of complex
networks to promote synchronization. When traditional optimization methods are
inapplicable, due to uncertain or unknown node dynamics, we propose a
data-driven approach leveraging datasets of relevant examples. We analyze two
case studies, with linear and nonlinear node dynamics. First, we show how
including node dynamics in the objective function makes the optimal graphs
heterogeneous. Then, we compare various design strategies, finding that the
best either utilize data samples close to a specific Pareto front or a
combination of a neural network and a genetic algorithm, with statistically
better performance than the best examples in the datasets.
