A recurrent neural network architecture is presented to learn the flow of a causal and time-invariant control system from data.For piecewise constant control inputs, we show that the proposed architecture is able to approximate the flow function by exploiting the system's causality and time-invariance.The output of the learned flow function can be queried at any time instant.We demonstrate the generalisation capabilities of the trained model with respect to the simulation time horizon and the class of input signals.