We present the MagNet, a neural network-based multi-agent interaction model to discover the governing dynamics and predict evolution of a complex multi-agent system from observations. We formulate a multi-agent system as a coupled non-linear network with a generic ordinary differential equation (ODE) based state evolution, and develop a neural network-based realization of its time-discretized model. MagNet is trained to discover the core dynamics of a multi-agent system from observations, and tuned on-line to learn agent-specific parameters of the dynamics to ensure accurate prediction even when physical or relational attributes of agents, or number of agents change. We evaluate MagNet on a point-mass system in two-dimensional space, Kuramoto phase synchronization dynamics and predator-swarm interaction dynamics demonstrating orders of magnitude improvement in prediction accuracy over traditional deep learning models.