Prediction and symbolification of optical chaos based on Kolmogorov-Arnold network

In this paper, we investigate the issue of optical chaos prediction in semiconductor lasers (SLs). We propose a neural network based on the Kolmogorov-Arnold representation theorem (KAN) for optical chaos forecasting. Compared with traditional reservoir computing (RC) models, the proposed network can learn the chaotic dynamics through learnable activation functions. The activation functions can be further sparsified and pruned, which greatly reduces the training overhead. Most importantly, the KAN after pruning can obtain symbolic expressions for the prediction of optical chaos, which significantly enhances the model's interpretability. Simulation results demonstrate that both the proposed KAN and the symbolified expression can predict optical chaos effectively, achieving a normalized mean square error (NMSE) less than 0.0022. Additionally, by varying the laser parameters, we validate the model's generalization capabilities under various conditions, with all NMSE values remaining below 0.01.