## 4 Results and Discussion  
Measures of accuracy for the confined compressive strength (\(f_{cc}\)) dataset employed for every algorithm are provided in Table 6. They can be examined in parallel to the identity plots of Figure 5, where \(f_{cc}\) experimental values are compared to \(f_{cc}\) predicted values, in terms of how close to the 45\({}^{\circ}\) line they stand. In cases where training and testing points are shown scarcely distributed away from the 45\({}^{\circ}\) line, this is evidence of poor fitting to the specific algorithm. It has been found that algorithms with a tree-like structure, such as RF, GBR, and DT, have demonstrated the best performance for all metrics for the compressive strength prediction, since all data points examined are set close to the 45\({}^{\circ}\) line. Satisfying results have also been calculated through the k-means and the MLP models. More specifically, the RF algorithm (Figure 5) achieves the highest \(R^{2}\) score, and this verifies that the implied regression model achieves fine fitting. This outcome agrees to the results obtained in [49], where RF has been found to provide accurate predictions in similar applications even with no parameter tuning. Fine fitting is further verified by the minimum values obtained for the absolute and the squared error, MAE and RMSE, respectively. The calculated AAD metric denotes that the variability of RF predicted values around the experimental ones is low. Another important evidence is the AIC value, which estimates the unknown parameters in terms of the Maximum Likelihood Principle [50]. In search of the best regression model, it is proposed that it is preferable to choose the one with minimum AIC value [51]. It is also important to note that our RF model achieves one of the highest accuracy metrics, compared to what is shown in the literature (more details can be found in the recent review of [PERSON] et al. [52]). The tree-based, ensemble GBR algorithm (Figure 5k), along with the DT (Figure 5i), have also performed similarly to RF, with high \(R^{2}\) score and low MAE, RMSE, and AAD values. The AIC criterion denotes slightly better performance for GBR compared to DT. Apart from the tree-based methods, the instance selection algorithm, k-NN, is also a good choice for predicting the compressive strength, followed by the polynomial-SVR. On the other hand, the remaining linear-based algorithms (MLR, Ridge, Lasso, in Figure 5a-c) and kernel-based (SVR-linear, SVR-rbf, GP, in Figure 5d,e,g, respectively) have shown smaller accuracy metrics. At first sight, this is evidence that the dataset incorporated clearly presents non-linear behavior. All linear ML algorithms have failed to reproduce the experimental data. On the other hand, kernel-based methods cannot be excluded from such applications, since they have shown remarkable performance in various material prediction models, especially in computationally intensive applications near the atomic scale [53; 54]. For the GP algorithm, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(R^{2}\) & **MAE** & **RMSE** & **AAD** & **AIC** \\ \hline MLR & 0.767 & 18.05 & 25.84 & 21.72 & 2755.38 \\ Lasso & 0.765 & 18.27 & 25.68 & 21.93 & 2753.81 \\ Ridge & 0.767 & 18.05 & 25.83 & 21.72 & 2755.33 \\ SVR-lin & 0.702 & 17.67 & 30.44 & 20.48 & 2846.65 \\ SVR-rbf & 0.825 & 17.32 & 26.06 & 20.33 & 2728.42 \\ SVR-poly & 0.918 & 9.94 & 16.24 & 11.37 & 2476.21 \\ GP & 0.758 & 19.91 & 26.92 & 25.23 & 2779.82 \\ k-NN & 0.921 & 10.27 & 15.59 & 12.30 & 2459.17 \\ DT & 0.933 & 8.92 & 14.64 & 10.47 & 2422.61 \\ RF & 0.957 & 7.52 & 11.58 & 8.82 & 2283.46 \\ GBR & 0.934 & 9.06 & 14.22 & 10.94 & 2404.13 \\ MLP & 0.919 & 10.89 & 15.79 & 12.52 & 2463.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Calculated metrics for all ML algorithms applied to the dataset for all eight inputs. of particular importance is how to select the kernel function and model parameters need to be recursively optimized to achieve the optimal result [38].