# Prediction of Microwave Characteristic Parameters Based on MMIC Gold Wire Bonding
## 3 Model and Analysis
### Building an Artificial Neural Network  
Neural networks, or artificial neural networks, are an algorithmic system developed by humans inspired by the structure of biological nerve cells [32]. The advantage of neural networks is that they can be built according to the constructed model, supervised continuous learning, and the flow diagram of the autonomously built artificial neural network model is shown in Figure 6:  
The number of neurons in the input layer is 6, and the number of neurons in the output layer is 123, including 6 hidden layers. The number of neurons and activation \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter Name** & **h** & **1** & **w1** & **w2** & **w3** & **w4** \\ \hline Minimum value & 0.1 mm & 0.3 mm & 1.841 mm & 0.192 mm & 1.593 mm & 0.267 mm \\ Maximum value & 0.2 mm & 0.6 mm & 2.241 mm & 0.392 mm & 1.993 mm & 0.667 mm \\ Spacing & 0.05 mm & 0.05 mm & 0.1 mm & 0.05 mm & 0.1 mm & 0.1 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of design parameters distribution for the structural model of wire bonding interconnect. function of each layer are shown in Table 2: Among them, the neurons are numbered h1-h6 from left to right, BN is Batch Normalization, which normalizes the value of the input activation function in the hidden layer and enables the data to be mapped to a reasonable interval without changing the data distribution characteristics. This makes the gradient training of hidden layer energy more stable during backpropagation and helps prevent overfitting of the neural network. Another way to prevent the neural network from overfitting is to introduce the Dropout mechanism. That is, for the hidden layer training, the internal neurons do not adopt the form of full connection with the next layer, but will randomly drop some of them, thus enhancing the generalization of the neural network and preventing overfitting. The initial learning rate is set to 0.0001, and the optimizer selects the adaptive optimizer Adam. This is an optimization function that automatically adjusts the learning rate according to the training process, which is more computationally efficient and less memory-demanding than other optimizers and generally does not require artificial parameter adjustments or just fine-tuning of the learning rate during the training process, which is very suitable for most of the application scenarios, especially those where the optimization objective is not known. MSE reflects the mathematical expectation of the square of the difference between the predicted value and the true value of the model. R-square indicates the degree of fit between the predicted value and the true value, and the value is between 0 and 1. The closer the R-square is to 1, the better the model fit is [33]. The formula for each evaluation index is shown below. \[MAE=\frac{1}{m}\sum_{i=1}^{m}\lvert y_{i}-\hat{y}_{i}\rvert \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Name** & **Input** & **h1** & **h2** & **h3** & **h4** & **h5** & **h6** & **Output** \\ \hline Number of neurons & 6 & 20 & 50 & 100 & 400 & 400 & 200 & 123 \\ Activation function & ReLU & ReLU & ReLU & ReLU & ReLU & ReLU & ReLU & \(\times\) \\ BN & \(\times\) & \(\times\) & \(\times\) & ✓ & ✓ & ✓ & ✓ & \(\times\) \\ Dropout & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & ✓ & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of neural network structure parameter. Figure 6: Schematic diagram of the process of the artificial neural network model. \[RMSE=\sqrt{\frac{1}{m}\sum_{i=1}^{m}(y_{i}-\hat{y}_{i})^{2}} \tag{2}\] \[R^{2}=1-\frac{\sum_{i-1}^{m}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{m} (y_{i}-\hat{y})^{2}}\] (3) \[MSE=\frac{1}{m}\sum_{i=1}^{m}(y_{i}-\hat{y}_{i})^{2} \tag{4}\]  
Equation (4) where m is the number of samples, \(y_{i}\) and \(\hat{y}_{i}\) are the true and predicted values of the ith sample, respectively, and \(\hat{y}\) is the average of the true values of the m samples.