A Review of Data-Driven Discovery for Dynamic Systems

Many real-world scientific processes are governed by complex non-linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non-linear dynamic systems using data-driven approaches. In this paper, we review the current literature on data-driven discovery for dynamic systems. We provide a categorisation 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.