We construct a data-driven dynamical system model for a macroscopic variable the Reynolds number of a high-dimensionally chaotic fluid flow by training its scalar time-series data. We use a machine-learning approach, the reservoir computing for the construction of the model, and do not use the knowledge of a physical process of fluid dynamics in its procedure. It is confirmed that an inferred time-series obtained from the model approximates the actual one and that some characteristics of the chaotic invariant set mimic the actual ones. We investigate the appropriate choice of the delay-coordinate, especially the delay-time and the dimension, which enables us to construct a model having a relatively high-dimensional attractor with low computational costs.

中文翻译：

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使用标量可观测的延迟坐标的宏观流体变量模型的机器学习构造

通过训练其标量时间序列数据，我们为宏观变量Reynolds数构建了一个数据驱动的动力学系统模型，该变量是高维混沌流体流的雷诺数。我们使用机器学习方法，即通过油藏计算来构建模型，并且在其过程中不使用流体动力学物理过程的知识。可以肯定的是，从模型中获得的推断时间序列近似于实际时间序列，并且混沌不变集的某些特征可以模仿实际时间序列。我们调查了延迟坐标，尤其是延迟时间和尺寸，这使我们能够构造具有低计算成本相对高维吸引模型的合适的选择。