## 3 Results
### Final Model Selection  
Figure 3 compares the performance of the seven models and visualizes the reliability of their predictions. By examining the scatter plots of the optimal models on the test set, both the model's performance and the reliability of its predictions can be evaluated. The distribution of the actual values and predicted values is displayed visually, and the regression line and error range of \(\pm\)10% show how well the predicted values fall within  
the acceptable range. The data points of XGBoost and LightGBM models are concentrated within the error range of 10%, indicating a better fit compared to the linear regression, SVR, KNN, decision tree, and random forest models. This suggests that the predictions of the XGBoost and LightGBM models can be considered more reliable compared to other models. Previous studies have also demonstrated similar findings. For instance, [PERSON] et al. [85] used machine learning to study fiber-reinforced concrete and found that both model data samples remained within the \(\pm\)10% deviation lines, while a study by [PERSON] et al. [71] on high-strength concrete prediction using LightGBM and XGBoost found a strong correlation between experimental and predicted results for both models. Figure 3: _Cont._  
Figure 4 compares the actual values and predicted values from the test dataset of seven optimal models. The horizontal axis represents the index of the test data, and the vertical axis represents the compressive strength. The data points connected by the red line represent the predicted values, while the data points connected by the blue line represent the actual values. A larger distance between the two data points on the y-axis indicates a lower accuracy of the model's predictions. From the analysis, it can be observed that both the XGBoost and LightGBM models fit the original data very well. Both models show high prediction accuracy between the data indices 50 and 100. Following that, the random forest and decision tree models also exhibit good alignment with similar results. The model with the highest error rate is the linear regression model, with errors evenly distributed across the entire data index. Based on these results, XGBoost and LightGBM models demonstrate high reliability, while the linear regression model shows the least reliable predictions. In Table 4, the values comparing the performance of the seven optimal models are presented, and Figure 5 illustrates the performance of the models based on Table 4. Through the comparison, the final model was selected based on performance metrics. Firstly, considering the R\({}^{2}\) values, the linear regression model had the lowest R\({}^{2}\) of 0.66 on the test set. In contrast, XGBoost and LightGBM models demonstrated strong predictive performance, achieving test set R\({}^{2}\) values of 0.93 and 0.94, respectively. This aligns with the findings of [85], who reported R\({}^{2}\) values of 0.93 for XGBoost and 0.94 for LightGBM. Secondly, looking at the RMSE and MAE values on the test set, the linear regression model  
Figure 3: Evaluation of the optimal model’s performance of (**a**) linear regression; (**b**) SVR; (**c**) KNN; (**d**) decision tree; (**e**) random forest; (**f**) XGBoost; and (**g**) LightGBM. had the highest values, while LightGBM had the lowest values of 4.16 MPa and 3.03 MPa, respectively, among the seven models. The RMSE and MAE values for the XGBoost and LightGBM models were also similarly low. Lastly, considering the Delta RMSE, the XGBoost model had a relatively low RMSE difference of 2.24 MPa, while the LightGBM model showed an even lower difference of 1.4 MPa. This indicates better generalization performance on the model. LightGBM exhibits high R\({}^{2}\) values on the test set along with low RMSE, MAE, and Delta RMSE values.