## 3 Results and Discussion
### Machine Learning to Predict \(q_{u}\) and \(E_{t}\)
#### 3.4.1 Comparison of Machine Learning Models
ANNs build complex input-output models that can learn intricate relationships within multidimensional data. Their widespread application spans a wide range of engineering disciplines [92; 93]. This paper will primarily focus on ANN-GMDH and ANN predictions using the TVT technique because it provides more consistent results than the K-fold for ANN predictions. ANN Models to Predict Elasticity Modulus (\(\mathbf{E_{t}}\))  
Figure 16 casts light on the regression cross plots of \(E_{t}\) model, which harnesses the power of artificial neural networks (ANNs) for elasticity modulus prediction. The figure delineates the congruence and disparities between true and predicted values across the training, validation, and test sets. Figure 16A-H highlights the precise predictions of ANN \(E_{t}\) models, displaying a favorable alignment with the x = y reference line and best fit trend line (ideal line) across a range of elasticity moduli [54]. In the training set, the \(E_{t}\) models achieve an R-squared of 0.9951 for ANN and 0.9963 for ANN-GMDH. the mean absolute error is 109.116 for ANN and 95.66 for ANN-GMDH, while the root-mean-square error (RMSE) is 145.4 for ANN and 125.67 for ANN-GMDH. This evidences the models' capability to apprehend intricate patterns within the training data and produce predictions that exhibit a commendable level of accuracy. In the validation set, the models maintain their predictive strength, achieving an R-squared of 0.9955 for ANN and 0.9956 for ANN-GMDH. The mean absolute error (MAE) is 108.792 for ANN and 96.658 for ANN-GMDH, while the root-mean-square error (RMSE) is 129.15 for ANN and 128.24 for ANN-GMDH. This highlights the models' proposes in extrapolating predictions to new data, with minimal deviations from the actual values. In the test set, consistent performance is observed, with an R-squared of 0.9924 for ANN and 0.9935 for ANN-GMDH. The mean absolute error (MAE) is 115.408 for ANN and 120.86 for ANN-GMDH, while the root-mean-square error (RMSE) is 170.03 for ANN and 157.31 for ANN-GMDH. This performance reiterates the models' proficiency in generating dependable predictions on independent data instances. When juxtaposed with SR model, it becomes apparent that ANN models occupy a favorable position. The ANN-GMDH model consistently outperforms the ANN model across all evaluation metrics, including R\({}^{2}\), MAE, and RMSE. However, it is important to note that the \(r_{d}\) value of the ANN-GMDH model is slightly worse than that of the ANN model. Overall, the ANN-GMDH model demonstrates better predictive accuracy and error minimization compared to the ANN model. The models aptly capture underlying relationships within the data and translates them into reliable predictions. This performance is poised to deliver valuable insights for elasticity prediction applications. ANN Model to Predict Unconfined Compressive Strength (\(q_{u}\))  
Figure 17 casts light on the regression cross plots of \(q_{u}\) model, which harnesses the power of artificial neural networks (ANNs) for unconfined compression strength prediction. The figure delineates the congruence and disparities between true and predicted values across the training, validation, and test sets. In Figure 17A-H, the ANN \(q_{u}\) models display precise predictions, aligning favorably with the x = y reference line and best-fit trend line (ideal line) across a range of unconfined compression strengths [54]. In the training set, the ANN model achieves an R\({}^{2}\) of 0.995 with an MAE of 19.471 and an RMSE of 28.54, while the ANN-GMDH model achieves an R\({}^{2}\) of 0.996 with an MAE of 17.73 and an RMSE of 25.54. This evidences the models' capability to apprehend intricate patterns within the training data and produce predictions that exhibit a commendable level of accuracy.