  Many real-world scientific processes are governed by complex nonlinear
dynamic systems that can be represented by differential equations. Recently,
there has been increased interest in learning, or discovering, the forms of the
equations driving these complex nonlinear dynamic system using data-driven
approaches. In this paper we review the current literature on data-driven
discovery for dynamic systems. We provide a categorization to the different
approaches for data-driven discovery and a unified mathematical framework to
show the relationship between the approaches. Importantly, we discuss the role
of statistics in the data-driven discovery field, describe a possible approach
by which the problem can be cast in a statistical framework, and provide
avenues for future work.
