This paper presents a computationally efficient wavefront aberration prediction framework for data-driven control in large-scale adaptive optics systems. Our novel prediction algorithm splits prediction into two stages: A highresolution and a low-resolution stage. For the former, we exploit sparsity structures in the system matrices in a data-driven Kalman filtering algorithm and constrain the identified gain to be likewise sparse; for the latter, we identify a denseKalman gain and performcorrections to the suboptimal predictions of the former on a smaller grid. This novel prediction framework is able to retain the robustness to measurement noise of the standardKalman filter in a much more computationally efficient manner, in both its offline and online aspects, while minimally sacrificing performance; its data-driven nature further compensates for modeling errors. As an intermediate result, we present a sparsity-exploiting data-drivenKalman filtering algorithm able to quickly estimate an approximateKalman gain without solving the Riccati equation.