Insect swarms are common phenomena in nature and therefore have been actively pursued in computer animation. Realistic insect swarm simulation is difficult due to two challenges: high-fidelity behaviors and large scales, which make the simulation practice subject to laborious manual work and excessive trial-and-error processes. To address both challenges, we present a novel data-driven framework, FASTSWARM, to model complex behaviors of flying insects based on real-world data and simulate plausible animations of flying insect swarms. FASTSWARM has a linear time complexity and achieves real-time performance for large swarms. The high-fidelity behavior model of FASTSWARM explicitly takes into consideration the most common behaviors of flying insects, including the interactions among insects such as repulsion and attraction, the self-propelled behaviors such as target following and obstacle avoidance, and other characteristics such as the random movements. To achieve scalability, an energy minimization problem is formed with different behaviors modelled as energy terms, where the minimizer is the desired behavior. The minimizer is computed from the real-world data, which ensures the plausibility of the simulation results. Extensive simulation results and evaluations show that FASTSWARM is versatile in simulating various swarm behaviors, high fidelity measured by various metrics, easily controllable in inducing user controls and highly scalable.