High-precision prediction and accurate replication of multi-dimensional correlation in strong and weak modes of the...

This paper proposes a photonic reservoir computing (PRC) framework with a dual-delay feedback structure. The framework uses chaotic dynamics of quantum-dot micropillar lasers (QDMLs) as nonlinear nodes. It achieves high-precision prediction of the temporal dynamics of strong modes (SMs) and weak modes (WMs) in mutually coupled QDMLs with time-delay feedback. It also accurately reconstructs the multi-dimensional correlation between these modes. We systematically analyze the effects of key PRC parameters on prediction accuracy. We evaluate the system robustness against variations in core physical parameters, including frequency detuning and feedback strength. The second-order correlation function is used to verify the prediction performance for the autocorrelation and cross-correlation of SMs and WMs. The results show that the predicted normalized mean square error (NMSE) is below 0.1 under optimized parameters. The prediction error of WMs is generally lower than that of SMs. The proposed system has good adaptability to fluctuations of core physical parameters. It can accurately replicate the evolution of multi-dimensional autocorrelation and cross-correlation of SMs and WMs with a feedback time delay.