Feed-forward Neural Networks with Trainable Delay

In this paper we build a bridge between feed-forward neural networks and delayed dynamical systems. As an initial demonstration, we capture the car-following behavior of a connected automated vehicle that includes time delay by using both simulation data and experimental data. We construct a delayed feed-forward neural network (DFNN) and introduce a training algorithm in order to learn the delay. We demonstrate that this algorithm works well on the proposed structures.