Nonlinear delay-embedded photonic reservoir computing for multi-step ahead prediction

Photonic reservoir computing exploits the nonlinear mapping capability of optical systems to enable efficient time-series processing, offering high speed, large bandwidth, and low power consumption. However, existing studies mainly focus on one-step prediction, while multi-step ahead prediction for nonlinear dynamical systems remains challenging. Here, we propose and experimentally demonstrate a nonlinear delay-embedded photonic reservoir computing (NDE-PRC), in which nonlinear combinations of delayed inputs are introduced to enhance multi-step ahead prediction. The resulting interwoven dynamics enrich the reservoir’s nonlinear complexity and memory capacity, enabling accurate multi-step prediction up to 20-steps with accelerated processing speed. Furthermore, the proposed approach exhibits improved robustness to system parameters, achieving reliable multi-step prediction over a significantly expanded parameter regime. Overall, our results demonstrate an effective and scalable approach for accurate and robust multi-step prediction of nonlinear dynamical systems, highlighting the potential of photonic reservoir computing for advanced temporal information processing.