In this paper, we propose SwarmNet -- a neural network architecture that can learn to predict and imitate the behavior of an observed swarm of agents in a centralized manner. Tested on artificially generated swarm motion data, the network achieves high levels of prediction accuracy and imitation authenticity. We compare our model to previous approaches for modelling interaction systems and show how modifying components of other models gradually approaches the performance of ours. Finally, we also discuss an extension of SwarmNet that can deal with nondeterministic, noisy, and uncertain environments, as often found in robotics applications.