## 5 Thermal Damage
### Machine Learning Techniques  
The compiled dataset was utilized to develop predictive models for thermal damage estimation using several supervised machine learning algorithms within the MATLAB (R2024b) environment, specifically via the Regression Learner Toolbox. The machine learning workflow consisted of the following key steps: data preprocessing, model selection, training, cross-validation, and performance evaluation. Initially, the dataset was prepared by ensuring consistency and removing any remaining anomalies or extreme outliers. No additional feature scaling or transformation was applied as the toolbox handles these internally when required. Several regression models were then trained, including Regression Tree (Fine Tree), Regression Tree (Coarse Tree), Artificial Neural Network (ANN), Gaussian Process Regression, Support Vector Machine (SVM), SVM (Medium Gaussian), Ensemble Boosted Trees, and Ensemble Bagged Trees. Since the original dataset had many missing points, only 136 full data points were used for model training. All models were trained using the default parameter settings provided by the toolbox. To ensure robust model evaluation and prevent overfitting, 10-fold cross-validation was employed during training. The performance of each model was assessed based on the coefficient of determination (R2) and the root mean square error (RMSE), which measure the proportion of variance explained and the average prediction error, respectively. The results, summarized in Table 4, indicated that model performance varied from fair to excellent, with R2 values ranging between 0.69 and 0.97, and RMSE values ranging from 0.0633 to 0.1902. Figure 5a-c provides representative plots comparing predicted and actual thermal damage values for selected models, visually illustrating the accuracy and reliability of the predictions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **R2** & **RMSE** \\ \hline Regression Tree (Fine Tree) & 0.94 & 0.0837 \\ Regression Tree (Coarse & 0.69 & 0.1902 \\ Tree) & 0.89 & 0.1110 \\ ANN & 0.97 & 0.0633 \\ Gaussian Process & 0.95 & 0.0790 \\ Regression & 0.91 & 0.1445 \\ SVM (Medium Gaussian) & 0.95 & 0.0741 \\ Ensemble Bagged Trees & 0.95 & 0.0767 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The performance of the predictive models.  
Figure 4: The correlation between the actual and predicted thermal damage.  
From Table 4, it can be seen that the Gaussian Process Regression is the best-performing model overall, with the highest R\({}^{2}\) and lowest RMSE values. Then, SVM, Ensemble Boosted Trees, and Ensemble Bagged Trees models equally showed the second-best prediction performance. Next, the Regression Tree (Fine Tree) model performed quite well, indicating strong predictive capability with relatively low error. However, among these top-five models, Gaussian Process Regression, SVM, and Ensemble Boosted Trees models predicted values slightly outside of the TD range: negative values or larger values than 1 (note that the TD, as per the definition, is between 0 and 1). Hence, despite their good prediction capabilities, these models cannot be suggested for TD prediction. As a result, the Ensemble Bagged Trees model (Figure 5a) and the Regression Tree (Fine Tree) model (Figure 5b) are considered the best. As an illustration of prediction outside the range, the Gaussian Process Regression model (Figure 5c) is given.