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.

流程图学习（FML）与深度神经网络（DNNs）相结合，已经展示出对未知动力系统的数据驱动建模的潜力。FML的一个显著特点是，在不存在精确的数学模型的情况下，它能够为部分观测到的系统产生准确的预测模型。本文概述了FML框架以及其成功实施的重要计算细节。我们还提供了一组明确定义的用于学习未知动力系统的基准问题。为了确保这些问题可以进行交叉验证并且结果可重现，所有这些问题的数值细节以及其FML的结果都已呈现出来。

未知动态系统的流图学习：概览、实现和基准测试