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We construct a data-driven dynamical system model for a macroscopic variablethe Reynolds number of a high-dimensionally chaotic fluid flow by training itsscalar time-series data. We use a machine-learning approach, the reservoircomputing for the construction of the model, and do not use the knowledge of aphysical process of fluid dynamics in its procedure. It is confirmed that aninferred time-series obtained from the model approximates the actual one ineach of various time-intervals, and that some characteristics of the chaoticinvariant set mimic the actual ones. We investigate the appropriate choice ofthe delay-coordinate, especially the delay-time and the dimension, whichenables us to construct a model having a relatively high-dimensional attractoreasily.

Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable