Machine-learning prediction of fluid variables from data using reservoir computing
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We predict both microscopic and macroscopic variables of a chaotic fluid flow using reservoir computing. In our procedure of the prediction, we assume no prior knowledge of physical model describing a fluid flow except that its behavior is complex but deterministic. We present two ways of prediction of the complex behavior; the first called partial-prediction requires continued knowledge of partial time-series data during the prediction as well as past time-series data, while the second called full-prediction requires only past time-series data as training data. For the first case, we are able to predict long-time motion of microscopic fluid variables. For the second case, we show that the reservoir dynamics constructed from only past data of energy functions can predict the future behavior of energy functions and reproduce the energy spectrum. This implies that the obtained reservoir system constructed without the knowledge of microscopic data is equivalent to the dynamical system describing macroscopic behavior of energy functions.
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