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

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, Lyapunov exponents, manifold structures, and statistical values. These dynamical characteristics can be reconstructed much more precisely by a data-driven model using reservoir computing than by computing directly from training data. With this idea, we estimate the state-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.