Predicting the largest Lyapunov exponent of chaotic optically injected lasers by machine learning

We demonstrate for the first time to our knowledge successful prediction of the largest Lyapunov exponent (LLE) for chaotic semiconductor lasers using a convolutional neural network. Chaotic emission intensity waveforms are first generated using an optically injected laser. For training the machine learning model, LLEs of different chaotic intensity waveforms are first calculated based on a traditional phase-space reconstruction method. After carefully optimizing the neural network operating parameters, the prediction of the LLE is found successful with an error of less than 5% in both simulations and experiments. Moreover, by using the proposed method for LLE estimation, the computation efficiency is effectively improved. As compared to traditional methods, the computation time is reduced from about 100 s to less than 1 s, while the required input data length is also reduced by 80%. The effects of laser inherent noise and measurement noise on the prediction performance are also investigated. The proposed method provides a new perspective on studying the laser dynamics.