## 3 Results
### Results of Simulating Three Types of Fibers Using a Single DeepONet Model  
As previously mentioned, the DeepONet architecture exhibits superior generalization capabilities compared to other models. To demonstrate this, we employed a single model to simultaneously simulate three distinct types of fibers: Normal Dispersion Fiber (NDF), High Nonlinearity Fiber (HNLF), and Standard Single-Mode Fiber (SMF). The trained model encompasses the parameter ranges of these three different fibers, as shown in Table 2.  
In the DeepONet model, both the Trunk and Branch Networks utilize a primary hidden size of 512 units. The Branch Network processes the initial pulse input, which has a size of 1024 points and 2 channels (representing the real and imaginary parts of the pulse). It starts with an initial convolutional layer that expands the 2 input channels to 512 channels using a kernel size of 7. This is followed by three residual blocks, each maintaining 512 channels, which help capture complex features from the input pulse. The output of these residual blocks undergoes global average pooling, followed by a final fully connected layer, which preserves the 512-unit representation. Similarly, the Trunk Network processes the fiber parameters, applying a self-attention mechanism and fully connected layers, also maintaining the 512-unit hidden size throughout the network. The Trunk Network handles the 5-dimensional fiber parameter input using a self-attention mechanism with a hidden size of 512 units. This is followed by three fully connected layers, each maintaining 512 units, allowing the network to capture intricate relationships within the fiber parameters. After processing through the Branch and Trunk Networks, the outputs are combined through element-wise multiplication. The resulting 512-dimensional vector is then passed through a multilayer perceptron. This perceptron consists of two hidden layers with 1024 units each, employing ReLU activations and dropout for regularization. The final output layer expands the representation to 2048 units, which is then reshaped to produce the 2 \(\times\) 1024 output that represents the real and imaginary parts of the propagated pulse. For dataset generation, we randomly selected various parameters within the entire possible range, including \(\beta_{2}\), \(\beta_{3}\), \(\beta_{4}\), and \(\gamma\), while maintaining the fiber length between 40 mm and 120 mm. The soliton order, being a derived quantity, varied as a result of the randomly selected parameters. This comprehensive approach ensured that our dataset covered a wide spectrum of possible fiber configurations and pulse propagation scenarios. We generated a total of 5000 datasets, divided into 4500 training sets and 500 test sets. The model was trained using the AdamW optimizer with an initial learning rate of \(1\times 10^{-3}\) and weight decay of \(1\times 10^{-5}\). We implemented a learning rate scheduler to adjust the learning rate based on the validation loss. The training process included early stopping with a patience of 30 epochs to prevent overfitting. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Pulse Width (ps)** & **Input Pulse Energy (pJ)** & **Fiber Length (cm)** \\ \hline
1 & 0.826419 & 2.622621 & 380 \\
2 & 0.662326 & 2.391764 & 470 \\
3 & 0.649601 & 2.647509 & 740 \\
4 & 1.069052 & 2.913348 & 1103 \\
5 & 1.174863 & 3.216344 & 1204 \\
6 & 0.689198 & 2.234762 & 1606 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pulse width, input peak power, and fiber length.