Fig. 3: Optical NGRC for Kuramoto-Sivashinsky time series forecasting.

a Experimental short-term prediction results of the Kuramoto-Sivashinsky (KS) time series with a domain size of L = 22 and a spatial sampling of S = 64. An optical NGRC with 2500 optical reservoir nodes is used for KS forecasting, which employs the current (u_t) and the previous (u_t−1) time steps in each training iteration for a total training length of 6000 time steps. The error subfigure (bottom) is the element-wise difference between the ground truth (top) and the experimental prediction (middle). The temporal axis is normalized by its largest Lyapunov time (λ_max = 0.043). b A part of the long-term prediction results by optical NGRC (between t₁ and t₂, where the prediction starts at t₀). Albeit the complete deviation between the KS ground truth (top) and the optical NGRC predicted output (bottom) at the element-wise level, the optical NGRC replicates the long-term behavior of the KS chaotic system. c The power spectra of the long-term prediction in (b) (red), the KS ground truth (blue) and a random noise signal (yellow). The power spectra of the ground truth and optical NGRC predictions are in good agreement, in stark contrast to the power spectrum of the random noise background