Predictive learning of multi-channel isochronal chaotic synchronization by utilizing parallel optical reservoir computers based on three laterally coupled semiconductor lasers with delay-time feedback.

In this work, we utilize three parallel optical reservoir computers to model three optical dynamic systems, respectively. Here, the three laser-elements in the response laser array with both delay-time feedback and optical injection are utilized as nonlinear nodes to realize three optical chaotic reservoir computers (RCs). The nonlinear dynamics of three laser-elements in the driving laser array are predictively learned by these three parallel RCs. We show that these three parallel reservoir computers can reproduce the nonlinear dynamics of the three laser-elements in the driving laser array with self-feedback. Very small training errors for their predictions can be realized by the optimization of two key parameters such as the delay-time and the interval of the virtual nodes. Moreover, these three parallel RCs to be trained will well synchronize with three chaotic laser-elements in the driving laser array, respectively, even when there are some parameter mismatches between the response laser array and the driving laser array. Our findings show that optical reservoir computing approach possibly provide a successful path for the realization of the high-quality chaotic synchronization between the driving laser and the response laser when their rate-equations imperfectly match each other.