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Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable. (English) Zbl 1467.76046

Summary: 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.

MSC:

76M99 Basic methods in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
68T05 Learning and adaptive systems in artificial intelligence
65P20 Numerical chaos
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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