# A Novel Physics-Guided Neural Network for Predicting Fatigue Life of Materials
## 3 Results and Discussions
Figure 7: The iterative process of the loss function of ANN and PGNN. function curve. Table 3 gives the predicted values of the fatigue parameters \(\sigma^{\prime}_{f}\),\(b\) for all the stress concentration factors \(\mathrm{Kt}\) and the stress ratio \(\mathrm{R}\) involved in the sample for the PGNN trained in Case 2. The predicted values of fatigue parameters in Table 4 can be used to further analyze the influence of loading environment on the change trend of fatigue life. This advantage of the machine learning method can provide help for scholars to study the fatigue phenomenon without carrying out a significant amount of fatigue experiments, saving time and resources. The sample set (\(\mathrm{Kt}=2.4\), \(\mathrm{R}=0.06\)) and (\(\mathrm{Kt}=3.4\), \(\mathrm{R}=0.74\)) are used as test samples to verify the data extrapolation ability of the PGNN method. Figure 9 shows the S-N curve of the test sample set generated by the PGNN. According to Figure 9, for the two test sample sets (\(\mathrm{Kt}=2.4\), \(\mathrm{R}=0.06\)) and (\(\mathrm{Kt}=3.4\), \(\mathrm{R}=0.74\)), the PGNN successfully predicted the corresponding S-N curve. It shows that the PGNN has a certain data extrapolation ability. It is worth mentioning that the data extrapolation ability of the PGNN proposed in this study is limited to the range of environmental factors that have been trained. In this study, it is the stress ratio and stress concentration factor. The addition of new environmental parameters such as temperature will lead to the retraining of the network, and all samples in the training set should contain temperature parameters. All environmental parameters must also adopt a unified unit of measurement. Therefore, this method can be used as a data extrapolation tool for fatigue tests, and environmental factors that are not included in fatigue tests cannot be evaluated. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Fatigue** \\ **Performance** \\ \end{tabular} } & \multicolumn{2}{c}{\(\mathrm{\mathbf{Kt}=1.6}\)} & \multicolumn{2}{c}{\(\mathrm{\mathbf{Kt}=2.4}\)} & \multicolumn{2}{c}{\(\mathrm{\mathbf{Kt}=3.4}\)} \\  & **(Stress Concentration Factor)** & **(Stress Concentration Factor)** & **(Stress Concentration Factor)** \\ \cline{2-7}  & \(\sigma^{\prime}_{f}\) & \(b\) & \(\sigma^{\prime}_{f}\) & \(b\) & \(\sigma^{\prime}_{f}\) & \(b\) \\ \hline (Stress ratio) & \(\mathrm{R}=-1\) & \(2.885\) & \(-0.117\) & \(2.938\) & \(-0.150\) & \(3.120\) & \(-0.195\) \\ \hline (Stress ratio) & \(\mathrm{R}=-0.37\) & \(2.911\) & \(-0.097\) & \(3.017\) & \(-0.141\) & \(3.201\) & \(-0.200\) \\ \hline (Stress ratio) & \(\mathrm{R}=0.06\) & \(2.889\) & \(-0.078\) & \(3.054\) & \(-0.137\) & \(3.237\) & \(-0.197\) \\ \hline (Stress ratio) & \(\mathrm{R}=0.46\) & \(2.894\) & \(-0.062\) & \(3.107\) & \(-0.132\) & \(3.271\) & \(-0.183\) \\ \hline (Stress ratio) & \(\mathrm{R}=0.74\) & \(\mathrm{R}=-\) & \(\mathrm{R}=0.101\) & \(3.260\) & \(-0.143\) \\ \hline (Stress ratio) & \(\mathrm{R}=0.85\) & \(\mathrm{R}=-\) & \(\mathrm{R}=-\) & \(\mathrm{R}=-\) & \(2.972\) & \(-0.063\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The predicted value of \(\sigma^{\prime}_{f}\), \(b\) outputted by PGNN. Figure 9: The predicted S-N curve of PGNN for the test set.