  We consider the problem of approximating flow functions of continuous-time
dynamical systems with inputs. It is well-known that continuous-time recurrent
neural networks are universal approximators of this type of system. In this
paper, we prove that an architecture based on discrete-time recurrent neural
networks universally approximates flows of continuous-time dynamical systems
with inputs. The required assumptions are shown to hold for systems whose
dynamics are well-behaved ordinary differential equations and with practically
relevant classes of input signals. This enables the use of off-the-shelf
solutions for learning such flow functions in continuous-time from sampled
trajectory data.
