  Dynamical systems see widespread use in natural sciences like physics,
biology, chemistry, as well as engineering disciplines such as circuit
analysis, computational fluid dynamics, and control. For simple systems, the
differential equations governing the dynamics can be derived by applying
fundamental physical laws. However, for more complex systems, this approach
becomes exceedingly difficult. Data-driven modeling is an alternative paradigm
that seeks to learn an approximation of the dynamics of a system using
observations of the true system. In recent years, there has been an increased
interest in data-driven modeling techniques, in particular neural networks have
proven to provide an effective framework for solving a wide range of tasks.
This paper provides a survey of the different ways to construct models of
dynamical systems using neural networks. In addition to the basic overview, we
review the related literature and outline the most significant challenges from
numerical simulations that this modeling paradigm must overcome. Based on the
reviewed literature and identified challenges, we provide a discussion on
promising research areas.
