## 3 Analysis and Discussion
### Numerical Analysis and Discussion  
In the numerical simulation, 5000 sets of random aberrations were generated, and the corrected voltage values were obtained by correcting the aberrations with the SGPD algorithm, and the voltage values were used as true values for the training of the neural network. To simulate real experiments, random noise was added. From these 5000 sets, 4000 sets served as the convolutional neural network's training data, and the remaining 1000 sets served as the network's testing data. The neural network was fed 128*128 pixel far-field spots and outputs 32-unit correction voltage values.  
The hyperparameters of the U-net network were set, as follows: The number of convolutional network layers was 22, the width was 64, the convolutional kernel size was 3, the convolutional step-size was 1, there was no padding, the pooling method was Max Pooling, the activation function was RuLe, the number of fully connected neurons was 638,976, the optimization algorithm was Adam, and the learning rate was the default.  
Compared with SGPD algorithm, the correction time of SGPD algorithm was 3.18 ms, while the neural network in this paper only needed 0.32 ms. Since the training data of the neural network was obtained from SGPD algorithm, the accuracy was not as high as SPGD algorithm. However, the correction accuracy and speed can be greatly improved by the method of coarse correction of neural network and fine correction of SPGD.  
Table 2 compares the performance of this paper's network Auto-U-net to that of a manually designed convolutional neural network (i.e., ResNet18, Inception v3, U-Net, EfficientNet-B0, and DenseNet). This illustrated the hyperparametrically optimized convolutional neural network performed significantly better in terms of the testing set and used fewer model parameters. As compared to the accuracy to the U-Net network, a 26 percent improvement was observed. A total of three convolutional network layers, a width of 32, three convolutional kernels, one convolutional step, no padding, Max Pooling as the pooling method, Tanh as the activation function type, 25,646 as the number of fully connected layer neurons, Adam as the optimization algorithm type, and 0.0045 as the learning rate were the optimized hyperparameters.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Hyperparameters**} & **Value Range of the Hyperparameters** \\  & **(Integer, Floating Point, Boolean, and Character)** \\ \hline Number of network stacking layers & 3–12 \\ Network width of each layer & 4–40 \\ Convolution kernel size & 1–7 \\ Convolution step size & 1–3 \\ Fill or not & 0 or 1 \\ Pooling mode & Max Pooling, verage Pooling, \\ Activation function type & Sigmoid, Tanh, ReLu, Leaky, ReLu, ELU \\ The number of neurons in the adequately & 256–1024 \\ connected layer & \\ Type of optimization algorithm & Adam, Sgd \\ Optimized the learning rate of the algorithm & 0.0001–0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hyperparameter types and their selection ranges.  
Figure 3 illustrates the comparison between the predicted value of the convolutional neural network after the hyperparameter optimization and the truevalue. Table 2 shows the RMSE values and the number of network parameters for the manually designed network and the network optimized by hyperparameters. It can be seen that the overall prediction effect was improved.