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

Kengo Nakai; Yoshitaka Saiki

doi:10.3934/dcdss.2020352

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arXiv · 1903.05770

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

Kengo Nakai·Yoshitaka Saiki

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Abstract

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 in each of various time-intervals, 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 easily.

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Kengo Nakai, Yoshitaka Saiki. 2019-03-14. Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable. https://doi.org/10.3934/dcdss.2020352

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