## 5 Results and Discussion  
### Building Response Prediction Models  
The ML algorithms described in the previous section were used to predict the seismic response (IDR) of the URM building, and their performance was assessed through the metrics developed based on the training set and the test set. The values of \(R^{2}\), adjusted \(R^{2}\), and RMSE associated with the prediction models are listed in Table 3. The following inferences can be drawn from the results of the prediction models:  
1. After examining several models, the RF, GPR, and NN models demonstrated effective performance in predicting the IDR of the URM building. This is evidenced by their higher \(R^{2}\) values and the lower RMSE values associated with the training data, the least being the RMSE of the RF model. However, the GPR model exhibits comparatively lower RMSE relative to the test data. The RF model showed a lower \(R^{2}\) value for the test set compared to the training set (3.6% reduction), indicating poor performance or high variance relative to the new dataset. On the other hand, the GPR model performed better in both the training and test sets (less than 0.2% variation), which is again evident from the RMSE values associated with the training and test sets of the model. This highlights the efficiency of GPR model in capturing the complex relationships in data. 2. The performance levels of the DT and SVM were found to be effective while examining the \(R^{2}\) and RMSE values of the training set. However, the results obtained from the test set of DT and SVM models showed a slightly poor performance, with comparatively smaller \(R^{2}\) values of 0.923 and 0.958, and larger RMSE values of 0.476 and 0.327, respectively, compared to other non-parametric models (RF, GPR, and NN). This indicates the overfitting of the DT model and the instability of the model relative to changes in the data. 3. The LR, SLR, and RR models are ineffective in accurately predicting structural response due to the nonlinearity in the relationship between the predictor and response variables. The findings also indicate a tendency for these linear models to overfit the data. The relatively poor performance of the linear models in comparison to their nonlinear counterparts may also be a result of their sensitivity to outliers in the seismic response data, despite the implementation of cross-validation and regularization techniques during the model development phase. 4. Even though the variation in the \(R^{2}\) value of the parametric models (LR, SLR, and RR) exhibits a variation from the best performing GPR model by 10% to 17%, a notable variation in the RMSE of the training set (55% to 65%) can be observed. This fact was also established by comparing the actual and predicted response (in natural logarithmic scale) of the test set obtained through various ML algorithms, as illustrated in Figure 8. It is also clear that non-parametric models, particularly the GPR model, show a much better fit. With its high RMSE values (0.70), and the least fit in the regression graph, the RR exhibits comparatively poor performance among the parametric models. The variations of the \(R^{2}\) and RMSE values associated with the prediction models are illustrated in Figure 9. The \(R^{2}\) values of the training and test sets for all the non-parametric models (DT, RF, SVM, GPR, and NN) ranged between 0.9 and 1.0, indicating the best performance, as compared to parametric models (LR, SLR, and RR). Furthermore, the RMSE values for SVM, GPR, and NN were all below 0.4, demonstrating their better performance. 6. Furthermore, the percentage variation in the \(R^{2}\) and RMSE values of the training and test sets of the ML models were calculated, and the results are compared in Figure 10. The lowest percentage variations for both the \(R^{2}\) and RMSE values were found in the GPR model, which again substantiates the effective performance of the model in predicting the response. Based on these results, the performance of SVM model was found to be relatively better than the DT, RF and NN models.