## 5 Results and Discussion
### Model Performance Evaluation
The ANN and MLP models have similar prediction accuracy but do not reach the levels of the GBDT, DT, and XGBoost models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & **MAPE (\%)** & **Score** \\ \hline ANN & \(5.5044\times 10^{-4}\) & 0.0235 & 0.0102 & 0.7872 & 3.1936 & 2 \\ DT & \(4.9854\times 10^{-7}\) & 0.0007 & 0.0002 & 0.9998 & 0.0602 & 6 \\ GBDT & \(6.7735\times 10^{-6}\) & 0.0026 & 0.0009 & 0.9974 & 0.2764 & 4 \\ KNN & \(8.5289\times 10^{-4}\) & 0.0292 & 0.0153 & 0.6703 & 5.0902 & 1 \\ MLP & \(4.5798\times 10^{-4}\) & 0.0214 & 0.0093 & 0.8230 & 2.9757 & 3 \\ XGBoost & \(1.8061\times 10^{-6}\) & 0.0013 & 0.0010 & 0.9993 & 0.3283 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation indices of six models in the training phase. Figure 8: Regression graphs of six prediction models using the training set: (**a**) ANN; (**b**) DT; (**c**) GBDT; (**d**) KNN; (**e**) MLP; (**f**) XGBoost. While the results obtained earlier provide valuable insights into each model's performance using the training set, they are not entirely sufficient for a comprehensive evaluation. Thus, the performance of all the developed models must be evaluated using the test set to ensure that the findings generalize well to unseen data. As shown in Figure 9, the KNN and MLP models show higher prediction accuracy in the testing phase than that obtained using the training set. Conversely, a notable decrease in the accuracy of the DT model during the testing phase suggests overfitting to the training phase. To combine the selection decisions from both phases, a ranking score was assigned to further evaluate model performance. Generally, the best model has the highest score among all models. The results listed in Table 6 show that the GBDT model obtained higher scores than the other models for all performance indices. Moreover, considering the ranking scores of all models obtained in the training phase, both the GBDT and XGBoost models achieved the same highest score of 10 among all models. This result shows that these two models have good learning ability and strong applicability. However, the GBDT model needs to be considered the best model overall since it demonstrated superior generalization in the testing phase. To further compare the predictive performance and agreement among the six ML models for thermal conductivity estimation, an analysis by Taylor diagram is conducted as shown in Figure 10. The Taylor diagram provides a comprehensive visual summary of model performance in terms of correlation, St. D, and RMSE. In the Taylor diagram, the model performance is represented by the distance between the model and the reference. Note that the reference position (red dot) corresponds to the observed data. It can be seen that the GBDT model is close to the reference point, indicating that its prediction performance is higher than the other models. This proximity to the reference point suggests that the GBDT model effectively captures the variability present in the observed data, demonstrating a high level of performance in this aspect. After this model, the XGBoost \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & **MAPE (\%)** & **Score** \\ \hline ANN & 8.7386 \(\times\) 10\({}^{-5}\) & 0.0093 & 0.0073 & 0.9664 & 2.4930 & 4 \\ DT & 2.8622 \(\times\) 10\({}^{-4}\) & 0.0169 & 0.0131 & 0.8900 & 4.4030 & 1 \\ GBDT & 1.0859 \(\times\) 10\({}^{-5}\) & 0.0033 & 0.0028 & 0.9958 & 0.9695 & 6 \\ KNN & 1.5440 \(\times\) 10\({}^{-4}\) & 0.0124 & 0.0099 & 0.9407 & 3.3441 & 2 \\ MLP & 1.2085 \(\times\) 10\({}^{-4}\) & 0.0110 & 0.0089 & 0.9536 & 2.9855 & 3 \\ XGBoost & 3.7124 \(\times\) 10\({}^{-5}\) & 0.0061 & 0.0051 & 0.9843 & 1.7921 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Evaluation indices of six models in the testing phase. Figure 9: Regression graphs of six prediction models using the testing set: **(a)** ANN; **(b)** DT; **(c)** GBDT; **(d)** KNN; **(e)** MLP; **(f)** XGBoost.