Optical Reservoir Computing Using Frequency Combs in Kerr Microresonators

Reservoir computing (RC) has been demonstrated in a variety of photonic platforms including fibers, resonators and free space optics implementations. Typically RC architectures exploit delay lines to provide memory and symbol interaction [1], [2]. In this work we propose an approach that eliminates this requirement by leveraging chaotic optical frequency combs (OFCs) generated via modulation instability (MI) in high-Q Kerr microresonators (MRs). We used the established mean-field Lugiato-Lefever equation (LLE)[3] to model the light dynamics inside the MR, demonstrating that unstable chaotic OFCs—traditionally considered unfit for applications—can exhibit computational capabilities. The system's performance was evaluated on prediction tasks of three benchmark dynamical systems: Mackey-Glass, Rössler, and Lorenz. Each 1700-symbol series was mapped to pump power values, modulating a continuous wave laser, driving a Kerr MR at 1 GSa/s. The MR's power spectral densities were used to construct a 1360 × 512 feature matrix, which was processed with linear regression for symbol prediction using an 80/20 training-to-testing split. Spectral features corresponding to the first symbol were used to predict the next one, with the predicted value fed back into the resonator to allow multi-step predictions up to 1200 symbols ahead as shown in Fig. 1 a)-c), which compare the true and predicted sequences for each system. These multi-step predictions were tested across 20 time-series, each obtained by seeding the dynamical systems with varying input conditions. Individual prediction errors <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varepsilon=\left\vert y_{\text {true }}-y_{\text {pred }}\right\vert$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y_{\text {true,pred }}$</tex> denote the true and predicted values respectively, are depicted as dots in panels d)-f). The 30%-70% percentile range shaded to indicate the error spread around the median. The lower x-axis represents the prediction depth in terms of symbols, while the upper x-axis corresponds to the internal time evolution of the dynamical systems.