## 4 Experimental Evaluation of the GAGAN Model
### Numerical Analysis
On the other hand, DCGAN models exhibited relatively lower g_loss values across the board, with DCGAN/3 and DCGAN/2 achieving g_loss values of 2.1455 and 2.5461, respectively, indicating more effective generators within the DCGAN framework. However, the consistently higher d_loss values for DCGAN models imply a weaker overall training process for the discriminator. For instance, DCGAN/5's d_loss of 0.5967 points to a less efficient discriminator, unable to effectively differentiate between real and synthetic images. Figure 8: Comparison of generator and discriminator loss for DCGAN and GAGAN. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Metric** & **g\_loss** & **d\_loss** \\ \hline DCGAN & Mean & 2.5420 & 0.4100 \\  & Variance & 0.1252 & 0.0121 \\ GAGAN & Mean & 7.1100 & 0.0690 \\  & Variance & 1.5986 & 0.0003 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean and variance of losses for DCGAN and GAGAN models. Table 4 presents a detailed comparison between DCGAN and GAGAN, using additional metrics alongside statistical analysis through \(p\)-values and confidence intervals (CIs). One notable limitation of GAGAN is its higher generator loss compared to DCGAN, with a mean generator loss of 7.110 versus 2.542. This indicates that GAGAN's generator faces greater difficulty in deceiving the discriminator. However, this is a direct consequence of the optimized GAGAN discriminator. The discriminator's enhanced ability to distinguish real from generated images creates a more challenging adversarial environment for the generator, making it harder for the generator to achieve lower loss values. Conversely, GAGAN's discriminator demonstrates superior performance, with a significantly lower mean loss of 0.069 compared to 0.410 for DCGAN. This demonstrates the exceptional performance of GAGAN's discriminator in identifying real versus generated images. This improvement is a result of using the GA that optimizes the discriminator's architecture and configurations, allowing it to better detect fine-grained differences between real and generated data. The statistical analysis supports these findings, with \(p\)-values for both generator and discriminator loss comparisons below 0.05, confirming that the observed differences are statistically significant. Furthermore, the 95% confidence intervals provide a range of plausible values for the true means, further reinforcing the reliability of these results. These metrics demonstrate both the challenges posed by the GAGAN's enhanced discriminator and the significant advantages of GA-based optimization in improving the model's overall performance. To further evaluate the image quality of both GAGAN and DCGAN models, two widely adopted metrics were used: Frechet Inception Distance (FID) and Inception Score (IS). FID measures the distance between the distributions of real and generated images, with lower values indicating higher similarity and quality. Table 5 presents the FID, the IS mean and the IS standard deviation (STD) values obtained after 50 epochs of training for both models. The IS mean represents the average score across multiple runs, reflecting the overall quality and diversity, while the IS STD quantifies the variability in the score, indicating the consistency of the model's performance. The results indicate that GAGAN significantly outperforms DCGAN in terms of FID and IS metrics. FID, a widely adopted metric that quantifies the similarity between the distributions of real and generated images (with lower values indicating better performance), \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Metric** & **Mean** & **CI (95\%)** & \(p\)**-Value** \\ \hline DCGAN & g\_loss & 2.5420 & 2.051–3.033 & 0.000 \\  & d\_loss & 0.4100 & 0.257–0.562 & 0.003 \\ GAGAN & g\_loss & 7.1100 & 6.156–8.063 & 0.000 \\  & d\_loss & 0.0690 & 0.057–0.081 & 0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical analysis of generator and discriminator losses for DCGAN and GAGAN.