## 5 Performance Evaluation of Seismic Response Prediction of ML Models
This inadequacy is likely due to the predominance of low-to-moderate seismic loads, which are more frequent in Korea, compared to the smaller number of strong seismic loads with high PGA. Table 8 presents four prediction performance evaluation indices for each model, offering a quantitative assessment of the accuracy of the ML models developed for predicting  
Figure 11: Comparison of prediction performance across six ML algorithms: (**a**) Decision Tree; (**b**) Random Forest; (**c**) Support Vector Machine; (**d**) k-Nearest Neighbor; (**e**) XGBoost; (**f**) neural networks. the seismic response of the NPP structure, considering aging deterioration. As demonstrated in Figure 11, the coefficient of determination (R\({}^{2}\)) for the DT model was the lowest among the six ML models, at 0.81. The R\({}^{2}\) values for the kNN and XGBoost models were 0.84 and 0.88, respectively, indicating slightly enhanced prediction performance compared to the DT model. The RF and SVM models both registered an R\({}^{2}\) value of 0.90; however, the RF model displayed a marginally lower MAE, indicating somewhat greater accuracy. Finally, the NN model recorded the highest R\({}^{2}\) value at 0.94, with the lowest values for the other error indices, quantitatively confirming its superior prediction performance among the six models. To ensure fair and consistent evaluation of all machine learning algorithms, the initial training phase focused on a single-output model that predicts the FRS at the uppermost floor (Z = 103 ft), where the maximum structural response typically occurs during seismic events. This simplified output setting was used across all six algorithms to facilitate a direct comparison of predictive performance. After identifying the NN model as the most accurate performer, the model was extended to a multi-output configuration to enhance its practical applicability. The multi-output NN model was designed to predict FRS values at three different floor levels simultaneously. This approach reflects the fact that seismic demands in NPP structures vary significantly across elevations. Figure 12 illustrates the network configuration of the NN model, which was optimized through the hyperparameter optimization process. The input layer consists of 13 ground motion characteristics and 4 material property alterations due to aging, totaling 17 nodes. The output layer delivers the acceleration spectrum for three target floors (Z = 103 ft, 84 ft, 66 ft), comprising a total of three nodes. The NN model comprises three hidden layers, with the node count optimized to 150, 150, and 100, respectively. The NN model developed is capable of simultaneously outputting the responses of the three considered floors. The responses from multiple output layers are compared with the corresponding target values as shown in Figure 13. As illustrated in the figure, the floor acceleration response spectrum shows an increase with floor height, indicating larger seismic responses for the upper floors. Despite variations in story heights, the responses of all three floors correlate well with their respective target values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ML** & **RMSE** & **MSE** & **MAE** & **R\({}^{2}\)** \\ \hline DT & 0.21 & 0.04 & 0.15 & 0.81 \\ RF & 0.15 & 0.02 & 0.11 & 0.90 \\ SVM & 0.15 & 0.02 & 0.12 & 0.90 \\ kNN & 0.19 & 0.04 & 0.13 & 0.84 \\ XGBoost & 0.17 & 0.03 & 0.13 & 0.88 \\ NN & 0.12 & 0.01 & 0.09 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the prediction performance indices of each ML model. Figure 12: Configuration of the multi-output NN model. Four performance evaluation indices for the NN model with three outputs, namely RMSE, MSE, MAE, and R\({}^{2}\), are 0.11, 0.01, 0.08, and 0.94, respectively.