## 3 Results and Discussion
### Machine Learning-Based Prediction of Thermal Conductivity  
Figure 11 illustrates the links between the experimental thermal conductivity (TC) and the predicted values obtained from machine learning (ML) models. This section sequentially evaluates the predictive capability of eight different ML methods for estimating the TC of foamed concrete [106]. During the training phase, SVM demonstrated the most accurate predictive performance, achieving a coefficient of determination R\({}^{2}\) of 0.9327. In contrast, KNNR and RF exhibited relatively poor and comparable prediction metrics, which may be attributed to their similar response mechanisms to specific data features [74; 113]. In the independent test set validation, the SVM model maintained its superior performance, resulting in an R\({}^{2}\) of 0.9148 and a mean absolute error of 0.0390 W/m\(\cdot\)K. The DTR model showed a substantial performance improvement on the test set, with the MAE decreasing from 0.0434 W/m\(\cdot\)K in the training set to 0.0220 W/m\(\cdot\)K--a reduction of 49.3%. The improvement is likely due to the model's inherent regularization effect, which mitigates overfitting. In contrast, the LMR model exhibited the poorest generalization capability [114; 115], with the test set R\({}^{2}\) dropping to 0.6264 and the mean absolute percentage error reaching as high as 67.71%. Figure 8: Regression graph for flexural strength. (**a**) SVR; (**b**) LMR; (**c**) RF; (**d**) DTR; (**e**) KNNR; (**f**) RR; (**g**) GPR; (**h**) NNR. Figure 9: Comparison of experimental and predicted flexural strength. (**a**) SVR; (**b**) LMR; (**c**) RF; (**d**) DTR; (**e**) KNNR; (**f**) RNR; (**g**) GPR; (**h**) NNR. As observed from Figures 12 and 13, the error decomposition analysis indicates that the prediction error primarily originates from systematic bias and random error. Among the models, RF exhibited the greatest overfitting tendency, with a \(\Delta\)R\({}^{2}\) of 0.0319, whereas KNNR demonstrated the most stable generalization performance, with a \(\Delta\)R\({}^{2}\) of 0.1784 [77; 116]. In the case of thermal conductivity (Figures 11-13), the support vector regression (SVR) model provides the most consistent and centrally distributed predictions, as observed by its tight clustering around the ideal prediction line and minimal variance across the dataset. This is further supported by its high coefficient of determination and low mean absolute error, suggesting strong generalization and stability across both low and high thermal conductivity ranges. In contrast, the Linear Multidimensional Regression (LMR) model exhibits large systematic deviations, especially in the lower and upper bounds  
Figure 11: Regression graph for thermal conductivity prediction. (**a**) SVR; (**b**) LMR; (**c**) RF; (**d**) DTR; (**e**) KNNR; (**f**) RR; (**g**) GPR; (**h**) NNR. Figure 10: Absolute error of flexural strength prediction. (**a**) SVR; (**b**) LMR; (**c**) RF; (**d**) DTR; (**e**) KNNR; (**f**) RR; (**g**) GPR; (**h**) NNR. of thermal conductivity values. The prediction points show a clear spread away from the diagonal reference line, indicating both underestimation and overestimation in different regions. This performance aligns with its relatively low R\({}^{2}\) and high MAPE values, which indicate poor fit and sensitivity to outliers or nonlinear behavior. Additionally, the Random Forest (RF) model demonstrates overfitting behavior, performing well in the training set but with increased dispersion and reduced accuracy in the testing set. The Decision Tree Regression (DTR) model, however, improves its accuracy in the testing phase, likely due to its built-in pruning mechanism, which reduces variance and enhances robustness. The KNNR and RR models show moderate performance, with noticeable fluctuations in sparse data regions, suggesting a dependency on local data structure and sensitivity to parameter scaling. Overall, these results confirm that some models perform better than others. SVR shows strong predictive accuracy for thermal conductivity.