# Machine Learning-Based Framework for Predicting Creep Rupture Life of Modified 9 Cr-1 Mo Steel
## 3 Results and Discussion
### Model Prediction Results  
After the feature screening process, the five essential features are identified and used for training various machine learning models. Figure 6 shows the \(R^{2}\) and \(RMSE\) of different machine learning strategies. Among the six algorithms, the GPR model with a Matern kernel function shows the best prediction accuracy because it displays the lowest \(RMSE\) and the highest \(R^{2}\), indicating that the GPR model is superior in capturing the complex nonlinear relationship between input features and creep rupture life. Although the SVR model with a polynomial kernel function shows a comparable \(R^{2}\) with GPR, its \(RMSE\) is slightly smaller than that of the GPR model. For other strategies, it is not unexpected that the Lasso and Ridge models perform worse than GPR and SVR models in terms of accuracy, because they are essentially linear regression models and cannot capture the inherent nonlinearity in the connections between creep life and input parameters. In addition, the DT model shows a relatively high \(R^{2}\) for the training set, while the value for the testing set remains the lowest. This indicates that the DT model is prone to overfitting, which has been also reported by previous studies [13; 23]. The RF model, an ensemble learning technique that functions by building a collection of decision trees during training, can reduce this problem. Consequently, the accuracy of the RF model is much higher than that of the DT model and comparable with that of the GPR and SVR models, as shown in Figure 6. In summary, based on the above results, the GPR model is selected as the optimum approach for the creep rupture life prediction of modified 9 Cr-1 Mo steel in this investigation. Figure 6: Comparison of accuracy for different machine learning models: (**a**) \(RMSE\) and (**b**) \(R^{2}\). Figure 7 displays the parity plots comparing the predicted creep rupture life to the actual values of modified 9 Cr-1 Mo steel using the GPR model with five key input features. The left plot shows the regression values obtained from both training and testing datasets. The prediction is more accurate as the data points approach the 45\({}^{\circ}\) line, as shown in Figure 7a. The RMSE values for the training and testing datasets are exceptionally low at 0.102 and 0.127, respectively. The comparison between the predicted creep life and actual creep life is displayed in Figure 7b, in which all data points are colored by the test stress at which the creep rupture experiments were carried out. Moreover, the second important feature, namely the test temperature, is quantified by the symbol size. Over the whole applied stress and temperature ranges, it is demonstrated that the GPR model offers excellent quantitative agreement. Furthermore, almost all the predicted data are distributed in the two-factor band line. It is also worth noting that the prediction accuracy and stability for long-term creep data (\(>\)10\({}^{4}\) h), which is the primary focus in structural integrity assessment and creep-oriented new alloy design, are both extremely satisfactory. These findings demonstrate that the GPR model provides high accuracy and good adaptability in predicting creep life under various environmental conditions. The prediction results of creep rupture life using the SVR model are shown in Figure 8 for comparison since the \(R^{2}\) of the SVR model is very close to that of the GPR model. Similarly, almost all creep data lie in the two-factor band line, as shown in Figure 8b, indicating adequate accuracy of the SVR model. However, compared to the predictions of the GPR model, an increasing proportion of data points are dispersed away from the 45\({}^{\circ}\) line as displayed in Figure 8a, leading to lower RMSE values for the SVR model.