A new data-driven method for latency compensation in adaptive optics sytems is developed and evaluated in this paper. Conventional adaptive optic controllers typically assume a single timestep of latency in the feedback loop, which is an appropriate assumption for low-frequency applications such as atmospheric optics compensation. However, the controller frequencies needed for aero-optic applications can approach the tens of kilohertz. Cumulative latency in the feedback loop originating from digital communication links, sensors, processing, etc. can exceed one timestep and thus significantly reduce the performance of adaptive optic controllers, even though open-loop frequencies of individual components are sufficiently fast for the application. Our method uses proper orthogonal decomposition as a basis for wavefront model reduction and an artificial neural network to predict the evolution of the associated modal coefficients over a short temporal horizon equivalent to the amount of latency present in the feedback loop. The method is capable of significantly augmenting the performance of conventional adaptive optics controllers. This algorithm has been evaluated in closed-loop simulation with disturbance data gathered from the Airborne Aero-Optics Laboratory. Over a 5-step prediction window, the new controller could reduce OPD rms in the worst cases by over 35%. Over a single timestep window, mitigations of greater than 55% are realized.