As modern data centers continue to grow in power, size, and numbers, there is an urgent need to reduce energy consumption by optimized cooling strategies. In this paper, we present a neural network-based prediction of air flow in a data center that is cooled through perforated floor tiles. With a significantly smaller execution time than computational fluid dynamics, it predicts in real-time server inlet temperatures and can detect whether prevalent air flow cools the servers sufficiently to guarantee safe operation. Combined with a cooling system model, we obtain a temperature and air flow control algorithm that is fast and accurate enough to find an optimal operating point of the data center cooling system in real-time. We also demonstrate the performance of our algorithm on a reference data center and show that energy consumption can be reduced by up to 30%.