## 2 Acquisition of Experimental Stress-strain Data  
The chemical compositions (wt %) of as-forged Ti-10V-2 Fe-3 Al alloy are as follows: V-10, Al-3.0, Fe-1.9, O-0.13, Si-0.05, C-0.05, N-0.05, H-0.0125, Ti (balance). The original as-forged Ti-10V-2 Fe-3 Al alloy was supplied in the form of bar with a diameter of 180 mm. The homogenized metal bar of Ti-10V-2 Fe-3 Al alloy was machined by wire-electrode cutting into several specimens with a height of 12 mm and a diameter of 10 mm, and the cylinder axes of these specimens are parallel to the axial line of the original bar. Figure 1 shows the optical microstructure of the original as-forged Ti-10V-2 Fe-3 Al alloy, in which the tiny acicular \(\alpha\)-phase grains dispersively distribute in the matrix of large \(\beta\)-phase grains. The transformation temperature from the (\(\alpha+\beta\)) phase to the \(\beta\)-phase of the alloy is about 1068 \(\pm\) 5 K. All of the specimens were homogenized under a temperature of 1033 K for 60 min. These specimens were compressed on a servo-hydraulic and computer-controlled Gleeble-3500 machine Dynamic Systems Inc., New York, NY, USA). The test samples were heated at a rate of 10 K/s and held at a certain temperature for 150 s to assure a uniform temperature and to reduce material anisotropism. The test samples were compressed with a height reduction of 60% (true strain 0.9) at the strain rates of 0.001, 0.01, 0.1, 1 and 10 s\({}^{-1}\) and the temperatures of 948, 973, 998, 1023, 1048, 1073, 1098 and 1123 K, and then, these deformed test samples were rapidly quenched into water to retain the microstructures acquired at high temperatures.  
Figure 2 shows the experimental compressive stress-strain curves of as-forged Ti-10V-2 Fe-3 Al alloy at different strain rates and temperatures. The variation of stresses with strain can be summarily classified into three stages. At the first stage, the stress quickly increases to a critical value with the increase of strain, where work hardening (WH) dominates this stage; at the same time, the stored energy in grain boundaries increases rapidly to the activation energy of dynamic recrystallization (DRX). At the second stage, DRX and dynamic recovery (DRV) occur and further grow, and the increasing rate of flow stress declines until a maximum stress where the thermal softening begins to exceed WH on account of DRX and DRV. The changes of stresses exhibit two types at the final stage: in the (\(\alpha+\beta\)) phase, the flow stress continuously declines with distinct DRX softening (948-1023 K and 0.001-0.1 s\({}^{-1}\)) [25]; the flow stress approximately maintains at a stable level where the \(\beta\)-phase predominates (1048-1123 K and 0.001-0.1 s\({}^{-1}\)), which indicates a new dynamic balance between WH and DRV [25]. The pre-existing literature demonstrates that there are close relationships among flow stress, strain rate and temperature. It is well known that stress-strain data play important roles in many areas, for instances speculating about WH and DRV [1], improving processing maps [3], characterizing dynamic recrystallization evolution [2], etc. A precise model of flow behaviors is critical to reflect material properties and to improve numerical simulation precision [26]. Thereby, it is important to establish a model to accurately characterize the highly non-linear flow behaviors.  
Figure 1: Optical photograph of the original as-forged Ti–10V–2 Fe–3 Al alloy.  
Figure 2: _Cont._  
Development of Support Vector Regression for the Hot Flow Behaviors of as-Forged Ti-10V-2 Fe-3 Al Alloy  
In this study, support vector regression (SVR) was used to establish a model to characterize the flow behaviors of as-forged Ti-10V-2 Fe-3 Al alloy on account of its excellent advantages of regression analysis ability, robustness and high efficiency.