【摘要】 畸形波(RWs)是超连续谱产生过程中的极端非线性事件。减速型有限能量艾里脉冲具有独特的自偏转演化特征,是探究RWs复杂动力学的理想物理载体。然而,传统上依赖求解非线性薛定谔方程来模拟该过程的计算成本极高,难以实时预测。为此,提出一种基于循环神经网络(RNN)和Transformer的混合神经网络演化预测框架。数值仿真表明,该框架不仅能够高精度地重构RWs的时空演化过程,准确预测RWs的判定阈值、激发个数等关键统计特征,还能有效捕捉极端事件的非线性动力学规律,为光学极端事件的研究提供高效且物理可解释的预测新范式。更多还原

【Abstract】 Objective Optical rogue waves(RWs) are extreme, rare, and highly destructive nonlinear events that spontaneously emerge during the process of supercontinuum(SC) generation in nonlinear fiber optics. Investigating these complex dynamics is of paramount importance for both fundamental physics and the design of high-stability optical systems. Recently, the decelerating finite-energy Airy pulse(FEAP) has garnered significant attention as a unique physical carrier. Unlike traditional symmetric pulses, the FEAP exhibits a highly asymmetric temporal profile. In the anomalous dispersion regime, the self-deflection of its main lobe allows the side lobes to act as seeds for modulation instability(MI), triggering intense soliton fission and Raman self-frequency shift, which ultimately excites RWs. Traditionally, research on these intricate dynamics relies on numerically solving the generalized nonlinear Schr??dinger equation(GNLSE). However, as rogue waves are rare statistical phenomena, capturing their extreme value characteristics accurately requires hundreds of independent repeated simulations under the same macroscopic initial conditions. This traditional numerical approach entails prohibitively high computational costs, making real-time early warning of extreme events challenging to implement. Furthermore, although deep learning methods have been introduced to the optical field, the excitation of RWs by decelerating FEAPs involves a profound coupling between higher-order dispersion and nonlinear effects. Most existing prediction schemes rely on singlestream deep neural networks for end-to-end deduction. Such monolithic architectures exhibit inherent limitations when confronting extreme nonlinear dynamics, particularly in predicting deterministic indicators such as extreme value thresholds. To address these challenges, we propose an efficient evolution prediction framework based on a hybrid recurrent neural network(RNN)-Transformer deep learning architecture. This framework aims to bypass the massive computational load of numerical solvers while accurately predicting both the spatiotemporal evolution trajectories and the complex statistical characteristics of optical RWs.Methods To generate a rigorous dataset, this study simulated the propagation dynamics of decelerating FEAPs in a photonic crystal fiber(PCF) using the GNLSE. The theoretical model comprehensively incorporated tenth-order dispersion, self-steepening, self-phase modulation, and Raman scattering, and introduced quantum noise to trigger MI. By varying the initial peak power and pulse width, we constructed a dataset comprising over a thousand independent spatiotemporal evolution samples. To quantitatively define the generation of optical RWs, four core statistical indicators were extracted: the maximum peak power of the output solitons, the RW generation threshold, the number of generated RWs, and the trailing ratio. On this basis, by incorporating multiple combinations of initial parameters and performing multiple independent simulations, a multi-dimensional dataset for these four statistical indicators was constructed. To predict these complex dynamics, a hybrid neural network architecture was constructed. This framework deeply integrated the local temporal memory capability of bidirectional long short-term memory(Bi-LSTM) networks with the global spatial attention mechanism of Transformer blocks. The Bi-LSTM layers bidirectionally scanned the spatiotemporal matrices within a fixed window to capture sequential dependencies, while the deep Transformer encoder blocks established long-range global dependencies by calculating correlation weights across different positions, thereby overcoming the distance decay limitation of standard recurrent networks. The model employed a three-layer fully connected decoding network with a decreasing number of neurons to extract extreme abrupt variation features. Furthermore, specialized loss functions, including a first-order gradient loss and a long-wavelength penalty loss, were utilized to compel the network to remain highly sensitive to rapid dynamic evolutions and extreme Raman redshifts in the spectral tail.Results and Discussions Simulation results demonstrated the high performance of the proposed framework. Physical investigations showed that as the incident peak power increased, the RW threshold and generation count rose significantly. Under high-energy excitation, the system reached an energy recombination critical point, resulting in a dispersed peak power distribution and complex soliton fission. Regarding spatiotemporal prediction, the hybrid model successfully reconstructed the long-distance deflection trajectories of FEAPs, pulse splitting, and soliton collisions. The predicted temporal and spectral evolutions aligned remarkably well with GNLSE simulations, with global errors maintained below 0.15. Crucially, the framework exhibited high accuracy in predicting statistical features. The peak power distribution curve was reconstructed with low root mean square error(RMSE), capturing the asymmetric L-shaped “long-tail” characteristic of RWs even under multi-parameter generalization tests. In the joint prediction of the four statistical indicators, the model maintained high stability even in chaotic terminal stages. For computational efficiency, while the traditional RK4IP method required approximately 20 s for a single simulation and took 1.6 h to complete an ensemble of 300 simulations, our hybrid model completed a single forward evolution in only 1.23 s. Furthermore, the statistical indicator prediction module could directly output results in less than 1 s, significantly saving computational time.Conclusions This study systematically investigates the physical mechanisms and statistical laws of RWs excited by FEAPs. The proposed RNN-Transformer framework successfully reconstructs complex spatiotemporal evolution processes and predicts multi-dimensional statistical features with high precision. The deep learning methodology shatters the computational barriers of traditional numerical methods, reducing statistical prediction time from hours to seconds. This acceleration provides a robust, physically interpretable, and computationally efficient new paradigm for real-time prediction and warning of extreme events in nonlinear optics. Future research will further optimize the network topology and expand its generalized application in more complex nonlinear optical systems.更多还原