Dynamical system analysis of a data-driven model constructed by reservoir computing

TL;DR

This paper analyzes data-driven reservoir computing models from a dynamical systems perspective, demonstrating their ability to accurately reconstruct complex dynamical features and predict fluid flow properties that are computationally expensive to simulate directly.

Contribution

It introduces a dynamical system analysis framework for reservoir computing models, showing they can accurately reproduce complex dynamical behaviors and predict fluid flow characteristics.

Findings

Data-driven models reconstruct dynamical features more precisely than direct data analysis.

Reservoir computing models can predict laminar lasting time distribution in chaotic flows.

The approach enables analysis of complex systems with high computational costs.

Abstract

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical characteristics can be reconstructed much more precisely by a data-driven model than by computing directly from training data. With this idea, we predict the laminar lasting time distribution of a particular macroscopic variable of chaotic fluid flow, which cannot be calculated from a direct numerical simulation of the Navier-Stokes equation because of its high computational cost.