Machine-learning inference of fluid variables from data using reservoir computing

TL;DR

This paper demonstrates that reservoir computing can infer microscopic and macroscopic fluid behaviors from complex data without prior physical knowledge, enabling long-term predictions and energy spectrum reproduction.

Contribution

It introduces two reservoir computing methods for fluid variable inference, one requiring partial data and the other only past data, without prior physical knowledge.

Findings

Long-time microscopic variable inference achieved.

Energy functions' future behavior and spectrum can be inferred.

Single measurement data can be used for time-series inference.

Abstract

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the complex behavior; the first called partial-inference requires continued knowledge of partial time-series data during the inference as well as past time-series data, while the second called full-inference requires only past time-series data as training data. For the first case, we are able to infer 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 infer the future behavior of energy functions and reproduce the energy spectrum. It is also shown that we can infer a time-series data from only one measurement by using the delay coordinates. These implies that the obtained two reservoir systems constructed without the knowledge of microscopic data are equivalent to the dynamical systems describing macroscopic behavior of energy functions.