  Flow map learning (FML), in conjunction with deep neural networks (DNNs), has
shown promises for data driven modeling of unknown dynamical systems. A
remarkable feature of FML is that it is capable of producing accurate
predictive models for partially observed systems, even when their exact
mathematical models do not exist. In this paper, we present an overview of the
FML framework, along with the important computational details for its
successful implementation. We also present a set of well defined benchmark
problems for learning unknown dynamical systems. All the numerical details of
these problems are presented, along with their FML results, to ensure that the
problems are accessible for cross-examination and the results are reproducible.
