## 2 Methodology
### Data Cleaning and Preprocessing  
In this study, the correlations and links between the material parameters of foam concrete and its mechanical strength and thermal conductivity were analyzed. The output parameters include compressive strength (Fc), flexural strength (Fr), and thermal conductivity (TC), all of which are functions of the input parameters, as shown in Equation (1). \[\mathrm{Output(F_{C},F_{r},TC)}\ =\mathrm{Input(Density,W/C,C,S/C,Cag/Fag,P,FA/C)} \tag{1}\]  
Table 1 presents the statistical characteristics of various parameters and their corresponding mechanical strengths and thermal conductivities. Figure 2 shows the statistical distributions of the material parameters, the corresponding mechanical strengths, and thermal conductivities. Despite some data scatter, a clear correlation is observed between the parameter variations and material performance indicators. To quantitatively assess this correlation, [PERSON]'s correlation coefficient is employed as a metric to calculate the linear relationship between the material parameters and the predicted values. Figure 1: Diagram illustrating the multi-stage process adopted to evaluate machine learning models. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Statistics** & **Density** & **W/C** & **Content** & **S/C** & **Cag/Fag** & **P (\%)** & **FA/C** & **Compressive** & **Flexural** & **Thermal** & **Conductivity** \\  & **(g/cm\({}^{3}\))** & **Ratio** & **(kg/m\({}^{3}\))** & **Ratio** & **Ratio** & **P (\%)** & **Ratio** & **Strength (MPa)** & **(MPa)** & **Coefficient** \\ \hline Mean & 1.53 & 0.41 & 414.94 & 0.99 & 0.43 & 37.61 & 0.22 & 24.15 & 2.63 & 0.15 \\ Max & 2.07 & 0.70 & 673 & 3.61 & 1.8 & 88 & 0.6 & 51.2 & 7.1 & 0.46 \\ Min & 0.43 & 0.26 & 120 & 0 & 0 & 8 & 0 & 15 & 0.2 & 0.04 \\ Range & 1.64 & 0.44 & 553 & 3.61 & 1.8 & 80 & 0.6 & 49.7 & 6.9 & 0.42 \\ Median & 1.65 & 0.35 & 445.5 & 1 & 0.4 & 32 & 0.18 & 26.06 & 2.66 & 0.16 \\ SE & 0.03 & 0.01 & 9.82 & 0.05 & 0.02 & 1.67 & 0.01 & 1.08 & 0.12 & 0.01 \\ Mode & 1.64 & 0.30 & 480 & 1 & 0 & 28 & 0.2 & 1.5 & 2.9 & 0.18 \\ Skewness & \(-\)1.21 & 1.35 & \(-\)0.72 & 0.61 & 0.78 & 0.79 & 0.57 & \(-\)0.16 & 0.29 & 0.85 \\ Kurtosis & 3.35 & 3.94 & 2.75 & 3.76 & 4.98 & 2.54 & 2.38 & 1.89 & 2.57 & 3.53 \\ SD & 0.43 & 0.12 & 0.12 & 0.68 & 0.31 & 21.91 & 0.14 & 14.01 & 1.55 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data statistical characteristics. Figure 2: _Cont._The Pearson correlation analysis was conducted to provide initial insights into the linear relationships between material parameters and target properties. However, it was not used as the sole basis for feature selection. All available parameters were retained as model inputs in order to capture both linear and nonlinear interactions through the machine learning algorithms. The correlation results mainly served to support the interpretation of feature influence and model behavior, particularly in the discussion of prediction accuracy and feature relevance. Although Pearson correlation coefficients were computed to assess the linear relationships between input variables and target properties, the results were not used to eliminate features. Instead, all parameters were retained in the modeling process to allow the algorithms to capture potential nonlinear effects and interactions. The correlation analysis primarily served to support a later interpretation of model outcomes. As shown in Figure 3, the correlation matrix reveals the complex interrelationships between the various parameters of foam concrete. The W/C exhibits a statistically significant inverse relationship with both compressive strength (Fc) and flexural strength (Fr), while the cement content shows a significant positive correlation with both. The thermal conductivity (TC) is crucially influenced by the foam concrete density, cement content, and the Cag/Fag. Significantly, there is a weak positive correlation between compressive  
Figure 2: Statistical characteristics of material parameters.