## 5 Applications of LHS-SVR in Material Computations  
The flow stress data at temperatures of 948 K-1123 K and strain rates of 0.005 s\({}^{-1}\), 0.05 s\({}^{-1}\), 0.5 s\({}^{-1}\), 0.5 s\({}^{-1}\) and 5 s\({}^{-1}\) were predicted for as-forged Ti-10V-2 Fe-3 Al alloy by the LHS-SVR. Additionally, the predicted stress-strain curves at a temperature of 1123 K and strain rates of 0.005 s\({}^{-1}\), 0.05 s\({}^{-1}\), 0.5 s\({}^{-1}\) and 5 s\({}^{-1}\) are shown in Figure 13. The expanded stress-strain curves are conducive to accuracy improvement in the following fields. In this section, the impact of input stress-strain curves on simulation results was analyzed in a compression experiment by the FEM software DEFORM version 6.1 (Scientific Forming Technologies Corporation, Columbus, OH, USA). The simulation parameters were set based on the actual experiments. One half of the metal sample was simulated for the reason of geometric symmetry, so as to decrease the computing time. In the actual experiments, the top and bottom surfaces of the metal sample were coated with graphite lubricants to decrease friction between the sample and anvils; thereby, the friction type between the contact surfaces of the sample and dies was set as shear-type in DEFORM. In the simulations, the heat conduction and heat radiation among metal sample, dies and the ambient were ignored to simulate the isothermal experimental compression test. If the finite element software needs to invoke stress-strain data that are not beforehand inputted into the software, the software mainly calculates unknown stress-strain data by mathematical interpolation means. However, hot flow behaviors of materials at different conditions (such as different strain rates and temperatures) are highly non-linear and complicated. The mathematical interpolation method cannot correctly predict the data of materials and will obtain inaccurate simulation results. Therefore, in this section, the expanded stress-strain curves predicted by LHS-SVR were applied to enrich the stress data of the Ti-10V-2 Fe-3 Al alloy. Two simulation schemes were designed to analyze the influences of input stress-strain curves on final simulation results. The entire initial conditions of the two simulation schemes are identical except for different input stress-strain curves. The compression tests were simulated at the temperature of 1123 K, the strain of 0.8 and a strain rate of 1 s\({}^{-1}\). The stress-strain curves at strain rates of 0.001-10 s\({}^{-1}\) and a temperature of 1123 K, which contain the predicted data, were applied to Scheme-A. The experimental stress-strain curves at strain rates of 0.001, 0.01, 0.1 and 10 s\({}^{-1}\) and a temperature of 1123 K were adopted by Scheme-B, so the stress-strain curve at a strain rate of 1 s\({}^{-1}\) and a temperature of 1123 K needs to be automatically interpolated by software. Figure 13: The true stress-strain curves of as-forged Ti–10V–2 Fe–3 Al alloy at a temperature of 1123 K and strain rates of 0.001 s\({}^{-1}\)–10 s\({}^{-1}\), in which the solid curves are experimental data and the fitted curves by points are predicted data. Figure 14a displays the distribution of the effective stress of Scheme-A, which can be approximately divided into three districts. Figure 14b displays the distribution of the effective stress of Scheme-B, which can be similarly divided into three districts. However, there are large differences of the distributions of effective stresses between Scheme-B and Scheme-A, as well as the average effective stress. In addition, as shown in Figure 15, the load curves corresponding to strokes of the top dies of these schemes show that the load curves of the top die of Scheme-A and the experimental values are very close. However, there are large differences of the top die loads between Scheme-B and the experimental values.