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We consider the problem of system identification of helicopter dynamics. Helicopters are complex systems, coupling rigid body dynamics with aerodynamics, engine dynamics, vibration, and other phenomena. Resultantly, they pose a challenging system identification problem, especially when considering non-stationary flight regimes. We pose the dynamics modeling problem as direct high-dimensional regression, and take inspiration from recent results in Deep Learning to represent the helicopter dynamics with a Rectified Linear Unit (ReLU) Network Model, a hierarchical neural network model. We provide a simple method for initializing the parameters of the model, and optimization details for training. We describe three baseline models and show that they are significantly outperformed by the ReLU Network Model in experiments on real data, indicating the power of the model to capture useful structure in system dynamics across a rich array of aerobatic maneuvers. Specifically, the ReLU Network Model improves 58% overall in RMS acceleration prediction over state-of-the-art methods. Predicting acceleration along the helicopter's up-down axis is empirically found to be the most difficult, and the ReLU Network Model improves by 60% over the prior state-of-the-art. We discuss explanations of these performance gains, and also investigate the impact of hyperparameters in the novel model.