We develop a neural model for dynamics in stabilized dense emulsions, which we train on data from first-principles simulations of biphase flows. From a physical perspective, a description at the level of droplets is an instance of modeling emergent phenomena in complex systems, with the ultimate goal of both developing physical insights and enabling more scalable simulation. From a machine learning perspective, modeling densely packed systems, with both elastic and plastic effects, serves as an interesting test case for neural models. We show that a naive approach, in which a graph neural network (GNN) predicts droplet displacements, leads to highly unstable trajectories. To overcome this problem, we develop a hybrid approach in which the GNN predicts corrections relative to a hand-crafted baseline model. We show that this hybrid model achieves both accurate and stable predictions. These preliminary results pave the way for a deeper understanding of emulsion physics as well as more computationally efficient numerical simulations.