Reservoir computers are a special type of recurrent neural network used for a variety of tasks including time series forecasting. The uncertainty of the forecast depends primarily on two quantities: the number of neurons $N$ comprising the reservoir computer and the number of training data $\ell$ comprising the time series. Under certain conditions, a central limit theorem applies causing the uncertainty on the forecast to converge to 0 with order $1/\sqrt{N}$ and $1/\sqrt{\ell}$ in the number of neurons $N$ and data points $\ell$.
The results hold for a broad class of time series, including ergodic dynamical systems arising from ODEs and stationary ergodic stochastic processes.

Remark: This seminar is a joint seminar with Kyoto University Applied Mathematics Seminar.