  Recurrent Neural Networks (RNNs) can encode rich dynamics which makes them
suitable for modeling dynamic systems. To train an RNN for multi-step
prediction of dynamic systems, it is crucial to efficiently address the state
initialization problem, which seeks proper values for the RNN initial states at
the beginning of each prediction interval. In this work, the state
initialization problem is addressed using Neural Networks (NNs) to effectively
train a variety of RNNs for modeling two aerial vehicles, a helicopter and a
quadrotor, from experimental data. It is shown that the RNN initialized by the
NN-based initialization method outperforms the state of the art. Further, a
comprehensive study of RNNs trained for multi-step prediction of the two aerial
vehicles is presented. The multi-step prediction of the quadrotor is enhanced
using a hybrid model which combines a simplified physics-based motion model of
the vehicle with RNNs. While the maximum translational and rotational
velocities in the quadrotor dataset are about 4 m/s and 3.8 rad/s,
respectively, the hybrid model produces predictions, over 1.9 second, which
remain within 9 cm/s and 0.12 rad/s of the measured translational and
rotational velocities, with 99\% confidence on the test dataset
