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

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