## 2 Acquisition of Experimental Stress-strain Data
### Comparisons of Study Abilities of the ANN, LHS-SVR and GA-SVR
The mathematical regression model cannot accurately track the hot flow behaviors, because the mathematical regression model has difficulty describing the complicated non-linear flow behaviors, which accompany phase transformation, WH, DRV and DRX in wide temperature and strain rate intervals. Worse still, the complicated calculation process of the mathematical regression model needs to be recomputed when some new experimental stress-strain data are involved. The LHS-SVR and GA-SVR do not need to establish the complicated mathematical models and the transformation mechanism of the micro structure. LHS-SVR and GA-SVR only need representative training samples from the study and then automatically adjust the three parameters \(C\), \(\gamma\) and \(\zeta\) to obtain the most accurate SVR. Comparisons of the Modelling Efficiencies of the Mathematical Regression Model, ANN, LHS-SVR and GA-SVR  
In Section 3.3, according to the preliminary search results where 1000 sample points were set in the intervals, \(C\in[0,100]\), \(\gamma\in[0,100]\), \(\zeta\in[0,100]\), only four \(R\)-values of the parameter combinations exceed 0.9999. In order to establish an accurate SVR model for as-forged Ti-10V-2 Fe-3 Al alloy, it is necessary to take much time and effort to manually adjust the three parameters one by one without using LHS-SVR. The intelligence algorithm LHS-SVR can automatically calculate the parameter combinations one by one in the search space to find the optimal value, which improves the computational efficiency to a certain extent. Based on the selection, crossover and mutation operators, the GA-SVR can self-adaptively and dynamically adjust the processes of selection, crossover and mutation and rapidly generates the optimal parameter combination. These processes of GA-SVR greatly improve the computational efficiency compared to LHS-SVR. Table 3 illustrates the time in modelling an accurate model of the mathematical regression model, ANN, LHS-SVR and GA-SVR. ANN needs to try many network topologies and training parameters to obtain an accurate model, which will consume much time and effort. The LHS-SVR and GA-SVR only need representative training samples from the research and then automatically adjust the three parameters \(C\), \(\gamma\) and \(\zeta\) to obtain the most accurate SVR. The modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model! ANN! LHS-SVR! GA-SVR. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model Phase**} & \multicolumn{3}{c}{_R-Value_} & \multicolumn{3}{c}{_AARE-Value_} \\ \cline{2-9}  & **Regression Model** & **ANN** & **LHS-SVR** & **GA-SVR** & **Regression Model** & **ANN** & **LHS-SVR** & **GA-SVR** \\ \hline \(\alpha+\beta\) & - & 0.99981 & 0.999962 & 0.999889 & - & 0.576\% & 0.090345\% & 0.510988\% \\ \(\beta\) & - & 0.99984 & 0.999964 & 0.999898 & - & 0.691\% & 0.186643\% & 0.669569\% \\ Strain of 0.5 & 0.9902 & 0.9998 & 0.999975 & 0.999923 & 6.583\% & 0.572\% & 0.074450\% & 0.529599\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The \(R\)-values and _AARE_-values of the testing dataset of the mathematical regression model, ANN, LHS-SVR and GA-SVR of the Ti-10V–2 Fe–3 Al alloy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Mathematical Regression Model**} & \multirow{2}{*}{**ANN**} & \multirow{2}{*}{**LHS-SVR**} & \multirow{2}{*}{**GA-SVR**} \\ \cline{2-2} \cline{6-7}  & & & & & & \\ \hline The time in modelling an accurate model & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The time in modelling an accurate model of the mathematical regression model, ANN, LHS-SVR and GA-SVR.