  We consider initial value problems of nonlinear dynamical systems, which
include physical parameters. A quantity of interest depending on the solution
is observed. A discretisation yields the trajectories of the quantity of
interest in many time points. We examine the mapping from the set of parameters
to the discrete values of the trajectories. An evaluation of this mapping
requires to solve an initial value problem. Alternatively, we determine an
approximation, where the evaluation requires low computation work, using a
concept of machine learning. We employ feedforward neural networks, which are
fitted to data from samples of the trajectories. Results of numerical
computations are presented for a test example modelling an electric circuit.
