## 4 Details of Machine Learning  
The composite material model established in this study is a multi-material composite structure influenced by multiple parameters. Given the complexity and non-linear interactions between material parameters, machine learning (ML) methods were applied to  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & **Factor A (Porosity)** & \
\begin{tabular}{c} **Factor B (Coating** \\ **Thickness)** \\ \end{tabular} &
\begin{tabular}{c} **Factor C (Fiber** \\ **Content)** \\ \end{tabular} \\ \hline
1 & 0 & 20 \(\upmu\)m & 0 \\
2 & 10\% & 60 \(\upmu\)m & 30\% \\
3 & 20\% & 100 \(\upmu\)m & 60\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Levels of factors in the orthogonal simulated calculation.  
analyze the effects of these parameters on thermal shock resistance by processing simulation data from various parameter combinations.  
The machine learning process involved the following steps: (1) establishment of the original dataset through simulations based on various parameter combinations. The variables include coating thickness, porosity, and fiber content; (2) preprocessing of the original dataset, which included normalization and removal of redundant features using a Pearson correlation coefficient threshold (e.g., \(\left|\,\mathrm{r}\,\right|>0.9\)); (3) a comparison of various ML algorithms based on three performance metrics--Mean Absolute Error (MAE), Mean Squared Error (MSE), and the coefficient of determination (R\({}^{2}\))--to identify the most accurate model; and (4) visualization of the influence of different features on the model's thermal shock resistance through feature importance ranking and SHAP (SHapley Additive exPlanation) analysis.  
Based on the simulation results presented in the previous section, we developed an initial dataset using three key input variables--coating thickness, porosity, and fiber content--with the SDEG of the coating as the output. The dataset consists of 40 sets of data. To ensure that the target attribute follows a normal distribution, we performed outlier detection and removal by visualizing the density and boxplots of SDEG [26]. Subsequently, all continuous variables were normalized to the range of 0 to 1 using the MinMaxScale [27]. This normalization approach eliminates unit-based discrepancies, enabling a comparison and appropriate weighting of metrics with different units or magnitudes. The MinMaxScaler operates according to Equation (8).  
\[X_{new}=\frac{X-\,X_{min}}{X_{max}-\,X_{min}} \tag{8}\]  
where \(X_{new}\) represents the normalized value, \(X\) denotes the raw data, and \(X_{max}\) and \(X_{min}\) are the maximum and minimum values of the dataset, respectively.  
Following normalization, a Pearson correlation analysis was conducted to evaluate the linear dependencies between features [28]. Pearson coefficients range from \(-1\) to 1, with values near \(\pm 1\) indicating strong linearity. Typically, features with coefficients above 0.9 in absolute value are considered redundant, and only one is retained to improve model interpretability. In this study, with a small number of features and all correlation coefficients below 0.8, no feature elimination was necessary.  
In this study, we compared several machine learning algorithms, including linear regression, ridge regression, random forest (RF), gradient boosted decision trees (GBDT), and XGBoost. All models were constructed using the scikit-learn package in Python 3.9.7 [27]. The dataset was split into training and test sets in an 80/20 ratio, and five-fold cross-validation was employed to mitigate overfitting [29]. Model performance was assessed using three key metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE), and the coefficient of determination (R\({}^{2}\)). MAE measures the average magnitude of prediction errors, MSE captures the squared differences between predictions and actual values, while R\({}^{2}\) evaluates the model's goodness of fit, with values closer to 1 indicating better predictive accuracy.