## 2 Materials and Methods
### The Proposed GAN-CSVR Model
#### 2.5.3 Step 3: Validation of the Augmented Data  
In the third step, the validation data is used to evaluate the performance of the model during training based on the loss function values. The validation of the performance for the GAN-CSVR model by using the Multi-Objective loss function, which combines MSE and BCE loss functions to assess structural differences and determine the similarity between augmented and validation data, has been applied. The validation process primarily focuses on evaluating the generated samples by the GAN-CSVR algorithm and assessing how well the generator has learned to capture and replicate the characteristics of the actual data distribution. The threshold value for the training and validation loss function with a discriminator is highly dependent on the distribution of data and the desired quality of the augmented data, initially starting with a threshold value between 0.1 and 0.5 and then adjusted based on the evaluation of the augmented data. The standard deviation and cumulative distribution functions have been used to assess the quality and fidelity of the generated samples, in addition to visual inspection, as explained in Section 4.1 in detail.  
The training and validation loss function values for the augmented and validation data have been compared. If the training loss function values are significantly lower than the validation loss function value it may indicate overfitting, where the model fits too closely to the augmented samples but does not generalize well to validation data. If the training loss function values closely match the validation loss values, augmented data are representative of the actual data distribution, and the Multi-Objective loss function is beneficial for improving generalization performance, and the augmented data will be accepted. The threshold between the training loss function values and the validation loss function values was determined as 0.2 based on the evaluation of augmented data, which achieved statistical similarity and pattern diversity for the augmented datasets. Finally, the GAN-CSVR model produces augmented samples that are fundamentally compatible with validation data and maintain representational characteristics without overfitting.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**GAN-CSVR** & **Layer 1** & **Layer 2** & **Layer 3** & **Layer 4** & **Optimizer** \\  & **CNN** & **CNN** & **CNN** & **SVR** & **Optimizer** \\ \hline \multirow{4}{*}{Generator} & Convolutional layer & Convolutional layer & & Noise dimension = 100 & \\  & filters = 64 & filters = 128 & Convolutional layer & Kernel type is RBF & \\  & Kernel size = 3 & Kernel size = 2 & & Regularization Parameter & \\  & Max pooling layer & Max pooling layer & & & (C) = 100 & \\  & RELU & RELU & & & epsilon = 0.01 & \\  & & & & Tolerance (tol) = & \\  & & & & & \(1\times 10^{-4}\). & \\ \hline \multirow{4}{*}{Discriminator} & Convolutional layer & Convolutional layer & & & \\  & filters = 64 & filters = 128 & & Kernel type is RBF & Adam \\  & Kernel size = 3 & Kernel size = 2 & & filters = 64 & \\  & Max pooling layer & Max pooling layer & & & epsilon = 0.01 & \\  & RELU & RELU & & Tolerance (tol) = & \\  & & & & \(1\times 10^{-5}\). & \\ \hline \end{tabular}
\end{table}
Table 1: The optimal parameter used in the GAN-CSVR model.