Reservoir computing is a machine learning technique which has been shown to
be able to replicate the chaotic attractor, including the fractal dimension and
the entire Lyapunov spectrum, of the dynamical system on which it is trained.
We quantitatively relate the generalized synchronization dynamics of a driven
reservoir computer during the training stage to the performance of the
autonomous reservoir computer at the attractor reconstruction task. We show
that, for successful attractor reconstruction and Lyapunov exponent estimation,
the largest conditional Lyapunov exponent of the driven reservoir must be
significantly smaller (more negative) than the smallest (most negative)
Lyapunov exponent of the true system. We find that the maximal conditional
Lyapunov exponent of the reservoir depends strongly on the spectral radius of
the reservoir adjacency matrix, and therefore, for attractor reconstruction and
Lyapunov exponent estimation, small spectral radius reservoir computers perform
better in general. Our arguments are supported by numerical examples on
well-known chaotic systems.

通过数量化的关联分析，我们发现驱动储层计算机的最大条件 Lyapunov 指数必须显著小于真实系统最小的 Lyapunov 指数，使得吸引子重构和 Lyapunov 指数估计得以成功，并且小谱半径的储层计算机通常在一般情况下表现更好。