Prediction of optical chaos using a multi-stage extreme learning machine with data uncertainty.

In this paper, we study the problem of predicting optical chaos for semiconductor lasers, where data uncertainty can severely degrade the performance of chaos prediction. We hereby propose a multi-stage extreme learning machine (MSELM) based approach for the continuous prediction of optical chaos, which handles data uncertainty effectively. Rather than relying on pilot signals for conventional reservoir learning, the proposed approach enables the use of predicted optical intensity as virtual training samples for the MSELM model learning, which leads to enhanced prediction performance and low overhead. To address the data uncertainty in virtual training, total least square (TLS) is employed for the update of the proposed MSELM's parameters with simple updating rule and low complexity. Simulation results demonstrate that the proposed MSELM can execute the continuous optical chaos predictions effectively. The chaotic time series can be continuously predicted for a time period in excess of 4 ns with a normalized mean squared error (NMSE) lower than 0.012. It also demands much fewer training samples than state-of-the-art learning-based methods. In addition, the simulation results show that with the help of TLS, the length of prediction is improved significantly as the uncertainty is handled properly. Finally, we verify the prediction ability of the multi-stage ELM under various laser parameters, and make the median boxplot of the predicted results, which shows that the proposed MSELM continues to produce accurate and continuous predictions on time-varying optical chaos.