## 3 Results  
### Prediction Results of High-Order Soliton Compression  
To train and test the capability of the neural network model in predicting nonlinear dynamics, we first simulated high-order soliton (HOS) compression under three random variable conditions. In these simulations, the fixed parameters included a step size of 0.13 cm for the Nonlinear Schrodinger Equation (NLSE) and a time window size of 10 ps. The variable parameters were as follows: pulse width (Full Width at Half Maximum, FWHM) ranging from 0.5 to 1.4 ps, input peak power ranging from 18 to 34 watts, and fiber length ranging from 0 to 20 m with a step size of 0.2 cm. The fixed parameters were as follows: Dispersion Coefficients \(\beta_{2}=-5.23\) ps\({}^{2}\)/km and \(\beta_{3}=4.27\times 10^{-2}\) ps\({}^{3}\)/km, and Nonlinear Parameter \(18.4\times 10^{-3}\) W\({}^{-1}\)m\({}^{-1}\). The Branch Network processes the initial pulse input, which comprises 2 channels (representing real and imaginary parts) with 1024 points each. It employs a convolutional layer that expands the 2 input channels to 256 channels, followed by two residual blocks, each maintaining 256 channels. The output undergoes global average pooling, and a final fully connected layer produces a 256-unit representation of the input pulse features. The Trunk Network is designed to process the single fiber parameter. It consists of a simple feedforward network with two fully connected layers, each containing 256 units and using ReLU activations. This network effectively captures the influence of the single parameter on pulse propagation. The outputs from the Branch and Trunk Networks are combined through element-wise multiplication, resulting in a 256-dimensional vector. This combined representation is then passed through a multilayer perceptron with one hidden layer of 512 units, followed by an output layer that produces 2048 units. These output units are reshaped to represent the real and imaginary parts of the propagated pulse (2 \(\times\) 1024). For our dataset, we generated 2000 samples by varying the chosen fiber parameter within its physically relevant range while keeping other potential variables constant. This dataset was split into 1800 training sets and 200 test sets, providing a robust basis for model training and evaluation. Figure 1(a) illustrates the temporal intensity evolution, and Figure 1(b) depicts the spectral intensity evolution of HOS propagation dynamics for a pulse width of 1.0 ps and an input peak power of 30 watts. As shown in Figure 3, the pulse propagation predicted by the neural network closely matches the pulse propagation simulated by the NLSE in both temporal and spectral intensity evolution. The narrowest pulse in the temporal intensity evolution corresponds to the broadest spectral width, indicating that the predicted maximum compression distance is accurate. Figure 1(c) provides a clearer depiction of the time-domain evolution as a function of propagation distance under these conditions. To facilitate a clearer visual comparison, we randomly selected pulses with pulse widths (FWHM) between 0.5 and 1.4 ps and input peak powers ranging from 18 to 34 watts for plotting. As illustrated in Figure 3, the corresponding parameters are detailed in Table 1. The substantial overlap of the full-time intensity pulses indicates the model's robust generalization ability and accuracy across various parameter variations. Figure 3: Comparison of the time intensity distribution predictions for different pulse widths (FWHM), input peak powers, and fiber lengths between SSFM results and model predictions. This figure showcases the accuracy and generalization capability of the model under various parameter settings. The Raman effect and self-steepening effect are both taken into consideration. Figure 2: Comparison of NLSE simulation and neural network prediction for high-order soliton (HOS) propagation dynamics with a pulse width of 1.0 ps and an input peak power of 30 watts.