## 3 Results and Discussion
### Validations and Analysis  
K-fold cross-validation is a rigorous model evaluation method that partitions the dataset into K mutually exclusive subsets {F1, F2,..., FK} [117]. Each subset is sequentially used as a test set, while the remaining \(\mathrm{K}-1\) subsets are combined to form the training set. This method ensures that each data is used in training K\(-\)1 times and in testing exactly once, thereby significantly improving data utilization [118]. Moreover, averaging the results across multiple independent tests effectively reduces the randomness and variance in the evaluation outcomes. In this study, a 5-fold cross-validation was employed to systematically examine the model's predictive quality [119]. As illustrated in Figure 14, the original dataset was stochastically divided into five non-overlapping and nearly equal partitions. During the validation process, each subset was used once as the test set, while the other four subsets served as the training set, resulting in five independent training-testing cycles. The procedure guarantees that every data sample is involved in four training phases and one testing phase. It allows for a comprehensive analysis of data dependencies while strictly adhering to the principle of independence in model validation. This section presents a comparative evaluation of the predictive performance of eight ML methods across different datasets. Key evaluation metrics include RMSE, MAE, MAPE, and R\({}^{2}\)[119]. These metrics were obtained after model training and are summarized in Figure 15. High R\({}^{2}\) values, along with low RMSE and MAE, are indicative of a robust predictive model, reflecting high accuracy and low residual error [120]. Different machine learning models in this study show distinct behaviors in terms of prediction accuracy and generalization. The Random Forest (RF) model performs well on the training set but shows a noticeable drop in accuracy on the test set. This indicates overfitting, where the model learns the training data too closely and fails to generalize to new data. Similarly, the K-Nearest Neighbors Regression (KNNR) model shows inconsistent performance, especially in areas with fewer data points. This is due to its sensitivity to local variations and its lack of a global learning strategy. In contrast, the Neural Network Regression (NNR) and Decision Tree Regression (DTR) models maintain relatively stable performance across both training and testing sets. These models demonstrate stronger generalization ability, likely due to their flexibility and ability to model complex nonlinear relationships. The Linear Multidimensional Regression (LMR) model performs poorly overall, with large errors  
Figure 13: Absolute error of thermal conductivity prediction. (**a**) SVR; (**b**) LMR; (**c**) RF; (**d**) DTR; (**e**) KNNR; (**f**) RR; (**g**) GPR; (**h**) NNR. and weak generalization, as it cannot capture nonlinear effects between variables. These differences highlight the importance of model selection based on both training performance and generalization capability. The results reveal that different performance indicators may favor different optimal models. Among the eight models evaluated, several techniques demonstrated distinct advantages worth deeper discussion. The Neural Network Regression (NNR) model consistently achieved the highest prediction accuracy for mechanical strength indicators. This can be attributed to its ability to capture complex nonlinear relationships, especially in datasets with multiple correlated input variables. The support vector regression (SVR) model showed superior performance in predicting thermal conductivity, likely due to the effectiveness of the quadratic kernel function in mapping input features into a higher-dimensional space. This kernel transformation was particularly useful in handling the subtle, nonlinear effects of parameters such as density and \(\mathrm{Cag}/\mathrm{Fag}\) on thermal conductivity.