## 4 Results and Discussion
### Performance of Models after Data Augmentation  
The data augmentation approach using the tabular GAN to generate synthetic samples led to substantial improvements in the predictive performance of all three models, as evidenced by Figure 7. The scatter plots show that the data points representing the predicted versus observed compressive strength values lie much closer to the ideal line after augmentation, indicating a stronger agreement between predictions and observations across the entire data range. The LightGBM and SVM models also exhibit improved performance with reduced scatter compared to their pre-augmentation results; their predictions still deviate more from the ideal line, particularly for higher strength values. For the CFNN model, the augmented data enabled the model to learn more robust patterns. This suggests that the CFNN model benefited more from the augmented data in capturing the underlying complexities and nuances of the problem. The tendency plots in Figure 7d-f further corroborate these observations. For the CFNN, the predicted values closely track the actual observed values across the entire test set, with minimal discrepancies on a sample-by-sample basis. In contrast, the LightGBM and SVM models, while improved, still exhibit noticeable fluctuations and deviations from the observed values, indicating a higher propensity for over- or underestimation on certain test samples. Figure 6: t-SNE visualization of the synthetic and original data. Also, the performance of the models is demonstrated in more detail in Table 6. Overall, the models achieved better performance after data augmentation. The CFNN model exhibited substantial improvements across all metrics after data augmentation. The \(R^{2}\) increased from 0.902 to 0.956 on the training set and 0.842 to 0.942 on the test set, indicating better explained variance and goodness of fit. The MAE decreased from 2.973 to 1.037 MPa on the training set and 3.940 to 1.546 MPa on the test set, representing reductions of 65.12% and 60.74% respectively. Similarly, the RMSE dropped from 3.348 to 2.982 MPa on the training set (10.9% reduction) and 6.442 to 3.836 MPa on the test set (40.5% reduction). The MAPE saw a notable decrease from 6.00% to 18.10% on the training set, though it improved from 18.00% to 5.283% on the test set. The RSR also reduced from 0.227 to 0.181 on the training set and 0.411 to 0.194 on the test set, indicating smaller errors relative to data variability. Overall, the CFNN demonstrated consistent and substantial improvements across all metrics after augmentation. For LightGBM, the \(R^{2}\) increased from 0.819 to 0.913 on the training set and 0.805 to 0.877 on the test set after augmentation. The MAE decreased from 4.357 to 3.004 MPa (31.1% reduction) on the training set and 5.593 to 3.366 MPa (39.9% reduction) on the test set. The RMSE also saw improvements, dropping from 6.287 to 4.676 MPa (25.7% reduction) on the training set and 7.240 to 4.657 MPa (35.6% reduction) on the test set. The MAPE decreased from 0.175% to 0.1% on the training set and 0.201% to 0.10% on the test set. Lastly, the RSR improved from 0.409 to 0.282 on the training set and 0.600 to 0.413 on the test set. While LightGBM showed improvements across all metrics, the magnitude of improvement was generally smaller compared to the CFNN model. The SVM model also benefited from data augmentation, with the \(R^{2}\) increasing from 0.893 to 0.922 on the training set and 0.783 to 0.863 on the test set. The MAE improved from 3.945 to 1.373 MPa (39.9% reduction) on the training set and 4.918 to 2.897 MPa (41.1% reduction) on the test set. The RMSE decreased from 5.277 to 3.256 MPa (38.2% reduction) on the training set and 7.309 to 5.61 MPa (23.2% reduction) on the test set. The MAPE  
Figure 7: Model performance after data augmentation. remained relatively unchanged at 0.06% on the training set but improved from 0.18% to 0.21% on the test set. Finally, the RSR saw improvements, decreasing from 0.333 to 0.281 on the training set and 0.411 to 0.399 on the test set.