Abstract: We present a biologically plausible dynamics model to simulate swarms of flying insects. Our formulation, which is based on biological conclusions and experimental observations, is designed to simulate large insect swarms of varying densities. We use a hybrid formulation that combines a force-based model to capture different interactions between the insects with a data-driven noise model, and computes collision-free trajectories. We introduce a quantitative metric to evaluate the accuracy of such multi-agent systems and model the inherent noise. We highlight the performance of our dynamics model for simulating large flying swarms of midges, fruit fly, locusts and moths. In practice, our approach can generate many collective behaviors, including aggregation, migration, phase transition, and escape responses, and we highlight the benefits over prior methods.