The research group of Professor Lilin Yi, Department of Electronic Engineering, Shanghai Jiaotong University (LIFE, Laboratory of intelligent fiber ecosystem) proposed a low-complexity ultrafast pulse nonlinear dynamic flexible prediction based on model-data hybrid drive, using a one-dimensional convolutional network (CNN ) feature decoupling modeling scheme, which realizes accurate prediction and flexible generalization of different pulse transmission scenarios, and the running time is reduced by 94% compared with the traditional split-step Fourier method. Compared with the recurrent neural network (RNN), An 87% reduction in run time was achieved using less than 1% of its parameters. Furthermore, during the prediction process, the input pulse conditions and transmission conditions can be accurately generalized, including pulse length, pulse width, peak power, and propagation distance. This work has significantly improved the various indicators of ultrafast nonlinear dynamic prediction based on AI algorithms, and also provided a new perspective of model-data-driven combination for the study of nonlinear characteristics in other fields. The relevant results were published in the international optical journal "Optics Express" in October 2022 under the title "Low-complexity full-field ultrafast nonlinear dynamics prediction by a convolutional feature separation modeling method". Yang Hang and Zhao Haochen are the co-first authors, and Professor Lilin Yi is the corresponding author.

Modeling and prediction of ultrafast nonlinear dynamics in optical fibers is essential for research in laser design, experimental optimization, and other fundamental applications. The traditional transport modeling scheme based on the nonlinear Schrödinger equation (NLSE) is time-consuming, and its application in parameter design and optimization experiments is limited. RNN has become a relatively accurate pulse amplitude prediction tool with low complexity and good generalization ability. However, the computational complexity and the flexibility of the neural network structure for longer input pulse lengths need to be further optimized to adapt to a wider range of application scenarios.

Research Path

Different from the traditional split-step Fourier method model-driven thinking, and the pure data-driven modeling scheme based on AI modeling, this research group explores the model-data hybrid-driven fiber channel modeling method, and autonomously transmits from the waveform by training the neural network. In the process, the physical interaction characteristics are speculated, and the feature-decoupled convolutional neural network is proposed as a new machine learning modeling model, and finally the simulation of the ultrafast pulsed optical fiber transmission phenomenon is realized. Here, the feature decoupling scheme means that linearity and nonlinearity in the fiber channel are modeled with different ideas. As shown in Figure 1a, the linear effect is linearly modeled by a model derived based on NLSE, and the nonlinear features are extracted from the data, and a 1D convolutional neural network is used for nonlinear modeling. Based on this, the time correlation in the data containing nonlinear effects is greatly shortened, which can greatly reduce the parameters, scale and operation time of the neural network. At the same time, feature decoupling can provide stronger model interpretability and better prediction accuracy.

In terms of data-driven nonlinear modeling, the research group started from the form of the physical equation of the traditional split-step Fourier method, analyzed its step-by-step solution process, and finally determined the modeling method based on the convolution structure. The schematic diagram of the network structure is shown in Figure 1b. A CNN-based new neural network structure suitable for ultrafast pulsed optical fiber transmission is designed. When designing the model, the nonlinear characteristics are considered to have the same operation logic for different pulse points. The designed CNN A large number of parameter sharing is realized in the structure, thereby further reducing the amount of parameters.

Compared with the previous purely data-driven method, the feature-decoupled CNN structure is closely integrated with the pulse transmission scene, and the sliding convolution kernel can adapt to the dynamic change of the input pulse length, providing better generalization ability. In addition, the influence of various hyperparameters in the structure on the introduction of the overall modeling is discussed in detail, and the optimal value is selected in the experiment, which is listed in the paper.

Research Results

Figure 2 shows the modeling effect of pulse transmission in a typical high-order soliton compression scenario. The waveform waterfall diagrams modeled by CNN and SSFM numerical methods are highly consistent, which proves the accuracy and effectiveness of CNN model modeling, which is sufficient to completely construct In the whole process of mode soliton transmission, several distances were selected for further comparison, and the frequency spectrum of the two corresponds to a high degree. Figure 3 shows the generalization ability of the CNN method for different input conditions. It shows that a single model can transmit the pulse characteristics and transmission distance generalization ability of a variety of inputs beyond the distance of the training data set. Compared with the traditional data-driven model The model method achieves a big improvement.

Figure 2   The effect of CNN modeling based on feature decoupling

Figure 3 Generalization performance of CNN model based on feature decoupling

On the basis of verifying the modeling accuracy and generalization performance of the model, and on the basis of theoretically analyzing the magnitude of changes in the amount of computation of the two, the experiment compares the computation time of CNN and SSFM to illustrate the effectiveness of this scheme in reducing complexity. Significant advantage. Limiting the use of only the CPU, a comparison is made from the perspective of the number of simulation points and the number of transmitted pulse groups, and the results are shown in Figure 4. It can be seen from the results that under the same conditions, the running time of CNN is greatly reduced compared with SSFM and the existing data-driven long-short memory network (LSTM) RNN method. In the supercontinuum 2048-point scene, the simulation of 100 sets of data is faster than the split-step Fourier method. 94%, compared with the previous LSTM-based method, using less than 1% of its parameters to achieve the same accuracy and 87% speed improvement, and can flexibly and dynamically adjust the input pulse width, intensity, input window length and transmission distance.

Figure 4  Comparison of running time between CNN method based on feature decoupling and existing methods under different data volumes

Compared with the traditional numerical simulation iteration scheme, the feature-decoupled CNN modeling scheme greatly reduces the complexity and running time. Compared with other data-driven models, it can better utilize the characteristics of the physical system, reduce modeling overhead, and realize The goal of fast and accurate prediction of the nonlinear dynamics of ultrafast pulsed fibers is achieved. In addition, the model also has generalization capabilities such as input points, input pulse parameters, and transmission distance, which can cover most scenarios of ultrafast pulse transmission modeling. This work is conducive to advancing the research on the phenomenon of ultrafast optical pulse transmission based on AI algorithms, and also demonstrates the application advantages of the model-data-driven combination method in traditional fields with prior knowledge.

Full text of the paper: https://opg.optica.org/oe/fulltext.cfm?uri=oe-30-24-43691&id=521706