## 2 Acquisition of Experimental Stress-strain Data
### Comparisons of Study Abilities of the ANN, LHS-SVR and GA-SVR  
The typical evaluation index of relative error (\(\delta\)) expressed as Equation (10) was utilized to estimate the performance of these prediction models. \[\delta\left(\%\right)=\frac{E_{i}-P_{i}}{E_{i}}\times 100\% \tag{10}\]  
where \(E\) is the sample of experimental stress-strain values; \(P\) is the sample of predicted stress-strain values; \(N\) is equal to the number of samples. Another evaluation index of average absolute relative error (\(AARE\)) expressed as Equation (11), as an average number of the absolute value of \(\delta\)-values, was adopted to further estimate the study abilities of these prediction models. Compared to \(\delta\)-value, \(AARE\) can better reflect total prediction error. \[AARE=\frac{1}{N}\sum_{i=1}^{N}\left|\frac{E_{i}-P_{i}}{E_{i}}\right| \tag{11}\]  
where \(E\) is the sample of experimental stress-strain values; \(P\) is the sample of predicted stress-strain values; \(N\) is equal to the number of samples. Figure 8 shows the \(R\)-values and \(AARE\)-values between the training samples and fitted values of the LHS-SVR and GA-SVR of the Ti-10V-2 Fe-3 Al alloy. The \(R\)-values and \(AARE\)-values between the training samples and fitted values of ANN, LHS-SVR and GA-SVR are listed in Table 1. As shown  
Figure 7: The relationships between the fitness values and the iteration times of GA-SVR. in Figure 8 and Table 1, it can be observed that the \(R\)-values between the training samples and fitted values of the LHS-SVR and GA-SVR model are larger than 0.9999, and the _AARE_-values of them are smaller than 0.402% of ANN. It can be summarized that LHS-SVR and GA-SVR can sufficiently and accurately learn the training samples. After comparisons of the \(R\)-values and the _AARE_-values of these models, it can be concluded that the study abilities of these models were shown as follows in ascending order: ANN < GA-SVR < LHS-SVR. Comparisons of the Generalization Abilities of the Mathematical Regression Model, ANN, LHS-SVR and GA-SVR  
Figure 9 shows the comparisons between the experimental flow stresses and testing flow stresses, which were predicted by the LHS-SVR and GA-SVR at different strain rates and temperatures. As shown in Figure 9, there is no singular point. The following work compared in detail the generalization abilities of LHS-SVR and GA-SVR. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **R-Value** & \multicolumn{4}{c}{**AARE-Value**} \\ \hline ANN & LHS-SVR & GA-SVR & ANN & LHS-SVR & GA-SVR \\
0.9999 & 0.999997 & 0.999961 & 0.402\% & 0.0599255\% & 0.379903\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(R\)-values and _AARE_-values between the training samples and fitted values of ANN, LHS-SVR and GA-SVR of the Ti–10V–2 Fe–3 Al alloy. Figure 8: The \(R\)-values and _AARE_-values between the training samples and fitted values by (a) LHS-SVR and (b) GA-SVR of Ti–10V–2 Fe–3 Al alloy. Figure 9: _Cont._  
Figure 10 shows the correlation between the experimental flow stresses and testing flow stresses of the LHS-SVR and GA-SVR model in the (\(\alpha+\beta\)) and the \(\beta\) phase, and the \(R\)-values of them are larger than 0.9998 at high accuracy levels. Figure 9: Comparisons between the trained flow stresses and the testing flow stresses predicted by LHS-SVR and GA-SVR at different strain rates and temperatures : (**a**) 948 K; (**b**) 973 K; (**c**) 998 K; (**d**) 1023 K; (**e**) 1048 K; (**f**) 1073 K; (**g**) 1098 K; (**h**) 1123 K.  
Figure 11 shows the correlation between the experimental stresses and testing stresses of the LHS-SVR and GA-SVR model at the strain of 0.5, and the \(R\)-values of them are larger than 0.9999 at high accuracy levels. In order to show in detail the distribution and the relative frequency of \(\delta\)-values of the LHS-SVR and GA-SVR at the strain of 0.5, they were further analyzed by Gaussian distribution analysis.