  Forecasting time series and time-dependent data is a common problem in many
applications. One typical example is solving ordinary differential equation
(ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is
not known explicitly and the ODE system is described by solution samples taken
at some time points. Hence, ODE solvers cannot be used. In this paper, a
data-driven approach to learning the evolution of dynamical systems is
considered. We show how by training neural networks with ResNet-like
architecture on the solution samples, models can be developed to predict the
ODE system solution further in time. By evaluating the proposed approaches on
three test ODE systems, we demonstrate that the neural network models are able
to reproduce the main dynamics of the systems qualitatively well. Moreover, the
predicted solution remains stable for much longer times than for other
currently known models.
