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Flow map learning (FML), in conjunction with deep neural networks (DNNs), hasshown promises for data driven modeling of unknown dynamical systems. Aremarkable feature of FML is that it is capable of producing accuratepredictive models for partially observed systems, even when their exactmathematical models do not exist. In this paper, we present an overview of theFML framework, along with the important computational details for itssuccessful implementation. We also present a set of well defined benchmarkproblems for learning unknown dynamical systems. All the numerical details ofthese problems are presented, along with their FML results, to ensure that theproblems are accessible for cross-examination and the results are reproducible.

Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks