## 3 Methodology  
### Based Method  
#### 3.1.1 Deep Neural Network  
The deep neural network (DNN) uses a fully connected network structure with a forward propagation computational algorithm. As shown in Figure 6, the DNN network model consists of an input layer, a hidden layer, and an output layer, where the number of neuron layers in the hidden layer is greater than 2.  
The neuron consists of five components, input, weights, bias, activation function, and output, as shown in Figure 7. Commonly used activation functions in neural network models are sigmoid, tanh, relu, leaky relu, etc. Equations (2) and (3) describe the linear regression and nonlinear activation of the neuron, respectively.  
\[y_{d}=\sum_{i=1}^{n}w_{l}^{ji}x_{l-1}^{i}+b_{l}^{j},\ (j=1,\ldots,n) \tag{2}\]  
\[\hat{y}_{l}^{j}=g(y_{d}) \tag{3}\]  
where \(y_{d}\) is the linear regression results of the \(j\)-th neuron in the \(l\) th layer. \(x_{l}^{j}\) is the output and nonlinear activation result in the \(l\)-th layer. \(w_{l}^{ji}\) is the weight corresponding to the \(i\)-th neuron in the \((l-1)\)-th layer. \(b_{l}^{j}\) is the bias of the \(j\)-th neuron in the \(l\)-th layer. \(g(\cdot)\) is the activation function.  
The evaluation of the performance of neural network models is crucial. The loss function is an important part of calculating the value that represents the distance between the predicted value and the target value. If the predicted value is far from the actual value, the larger the value of the loss function will be; if the predicted value is accurate, the  
Figure 6: DNN model composition.  
smaller the value of the loss function will be. The loss function determines the optimization of the parameters within the neural network model and serves to measure the overall quality of the model's predictions. The commonly used loss functions are mean square error (_MSE_), mean absolute error (_MAE_), root mean square error (_RMSE_), and coefficient of determination (\(R^{2}\)).  
\[MSE=\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}(m_{i}-p_{i})^{2} \tag{4}\]  
\[MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}|m_{i}-p_{i}| \tag{5}\]  
\[RMSE=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}(m_{i} -p_{i})^{2}} \tag{6}\]  
\[R^{2}=\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}\left(p_{i}-m_{i} \right)^{2} \tag{7}\]  
where \(m_{i}\) is the value of the measurement. \(p_{i}\) is the value of the prediction model.\(\overline{m}\) is the average value of the measurement. \(n\) is the total number of the dataset.  
The DNN model is trained by the gradient descent method to reduce the loss function value of the model. Gradient descent training can be divided into two stages. The first stage is to find the loss function going forward. The second stage backpropagates to find the gradient of each neuron weight and bias and then updates the weights and biases according to the chain derivation law of the composite function, as shown in Equation (8).  
\[\left\{\begin{array}{l}\widetilde{w}_{l}^{ji}=w_{l}^{ji}-\alpha\left.\frac{ \partial L}{\partial w}\right|_{w=w_{l}^{ji}}\\ \widetilde{b}_{l}^{-j}=\left.b_{l}^{j}-\alpha\left.\frac{\partial L}{\partial w }\right|_{b=b_{l}^{j}}\end{array}\right.\right. \tag{8}\]  
where \(\widetilde{w}_{l}^{ji}\) and \(\widetilde{b}_{l}^{-j}\) are the updated weight and bias, respectively. \(\alpha\) is the learning rate, which is one of the parameters that control the extent of parameter update. \(L\) is the loss calculated by Equations (4)-(7).