## 3 Results
### Experiment 1 and Experiment 2 Comparative Analysis  
In Experiment 1, a 10-fold cross-validation approach was used to evaluate the performance of the model under different hyperparameter configurations. The parameters considered include the number of layers (_NumLayers_) from 1 to 2, activation functions (activations) including'relu', 'tanh','sigmoid' and 'none', standardization (standardize) options of 'true' or 'false', regularization parameter (lambda) with values between 1.9172 \(\times\) 10\({}^{-9}\) and 0.1, and the sizes of Layer 1 and Layer 2 ranging from 1 to 300. In Experiment 2, a 5-fold cross-validation was performed to evaluate the robustness of the model under the same hyperparameter variations. These experiments aimed to systematically investigate  
Figure 4: Performance evaluation of Model II (model4301) on an unseen new test dataset. the effects of different configurations on the predictive performance of the model and to gain insights into the optimal hyperparameter settings for each regression task. The process of identifying the optimal model for predicting hardness in the regression task involved three important steps. First, the fifteen best-performing models from each experiment were selected, highlighting their performance in the test datasets. Then, the selection was refined to the five best models. The results are shown in Tables 5 and 6. In the final stage, a comparative analysis was performed between the best model from each experiment and the best models from the training datasets. Ultimately, the most effective test model was identified for subsequent prediction and deployment. These results provide a comprehensive insight into the performance of the models under different cross-validation schemes and help to select the most effective models for predicting hardness in the regression task. Based on the metrics provided in Table 7 and Figures 5 and 6, Model 4208 appears to outperform the other models, except for in terms of the mean absolute error (MAE). It achieves a relatively low MSE of 1.1643, indicating its ability to minimize the squared differences between predicted and actual values. The root mean squared error (RMSE) is also comparatively low at 1.0790, indicating accurate predictions with less variability. Although the MAE is slightly higher compared to some other models, it is still reasonable at 0.6938, indicating a relatively small average absolute error. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Activation**} & \multirow{2}{*}{**Lambda**} & \multirow{2}{*}{**L1**} & \multirow{2}{*}{**L2**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**R2**} & \multicolumn{2}{c}{**MSE**} & \multicolumn{2}{c}{**MAE**} \\ \cline{5-10}  & & & & & **Train** & **Test** & **Train** & **Test** & **Test** \\ \hline Model 4301 & ‘sigmoid’ & 0.000185376 & 93 & 120 & 1.0690 & 1.0976 & 0.9907 & 0.9896 & 1.2046 & 0.7101 \\ \hline Model 4303 & ‘sigmoid’ & 0.000136655 & 116 & 112 & 1.0768 & 1.0826 & 0.9906 & 0.9899 & 1.1720 & 0.6885 \\ \hline Model 4307 & ‘sigmoid’ & 0.000224495 & 82 & 123 & 1.0968 & 1.1109 & 0.9903 & 0.9894 & 1.2340 & 0.7269 \\ \hline Model 4308 & ‘sigmoid’ & 8.70 \(\times\) 10\({}^{-5}\) & 91 & 153 & 1.0971 & 1.0830 & 0.9903 & 0.9899 & 1.1729 & 0.6937 \\ \hline Model 4314 & ‘sigmoid’ & 0.000146841 & 87 & 167 & 1.1033 & 1.0982 & 0.9901 & 0.9896 & 1.2059 & 0.7040 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The five best models from Experiment 1 (5-fold CV).