## 1 Introduction
further pointed out that the original Johnson-Cook model was not able to predict the softening part of the flow stress curves [16]. The mathematical regression equations of the phenomenological model cannot accurately track the highly non-linear flow behaviors at different strain rates and temperatures [15; 17]. Because they are mathematically fitted based on limited experimental data. lately, the artificial neural network (ANN) of intelligence algorithm, which imitates biological neural systems, was adopted to characterize the flow behaviors of AZ80 magnesium alloy [18], A356 aluminum alloy [19], Ti-10V-2 Fe-3 Al alloy [20], etc. ANN needs to try many network topologies and training parameters to achieve a higher accuracy, which will consume much time. For a certain dataset, the identical network topology and training parameters of an ANN will obtain fluctuant accuracies in different attempts. ANN can meet network topology and training parameters well to achieve a higher accuracy level; however, these accurate results have poor reproducibility. Worse still, ANN easily falls into local extreme values and cannot attain a globally-optimal solution. Support vector regression (SVR), as a machine learning method according to the structural risk minimization principle and statistical learning theory, is mostly used in the regression analysis field [21]. SVR has the advantages of strong generalization ability, robustness and a systemic theoretical system. Compared to ANN, SVR can avoid falling into local extreme values and can attain a globally-optimal solution. For a certain dataset, an SVR with identical training parameters will maintain training accuracy and prediction accuracy at stable levels in different attempts. In this work, SVR was adopted to characterize the hot flow behaviors of as-forged Ti-10V-2 Fe-3 Al alloy on account of its excellent advantages. The learning ability and generalization ability of an SVR rely on three parameters (penalty factor \(C\), kernel parameter \(\gamma\) and insensitive loss function \(\zeta\)), especially the mutual impacts among them. Therefore, SVR needs to adjust the three parameters (\(C\), \(\gamma\) and \(\zeta\)) to attain a precise prediction model. An SVR with appropriate parameters \(C\), \(\gamma\) and \(\zeta\) will accurately study the stress-strain curves and appropriately ignore some singular points of stress-strain data to accord with the overall trend of the curves. The influence of the combination of the three parameters (\(C\), \(\gamma\) and \(\zeta\)) on the learning ability and generalization ability of an SVR should be synthetically considered. It is time consuming to independently adjust the three parameters one by one to establish an SVR that can accurately characterize the hot flow behaviors of as-forged Ti-10V-2 Fe-3 Al alloy. Thereby, it is important to find a stable and efficient method to realize the optimal selection of the three parameters in SVR. [PERSON] et al. established an SVR combined with particle swarm optimization (PSO) to characterize the flow behaviors of AZ80 magnesium alloy in which PSO was adopted to select the parameters \(C\), \(\gamma\) and \(\zeta\), and this study indicates that the model is more accurate than ANN and the constitutive equation; besides, the sample dependence of the SVR is lower [22]. [PERSON] et al. constructed an SVR to characterize the flow behaviors of Austenitic Stainless Steel 304, and they found that SVR is more precise, efficient and reliable than the mathematical regression equations, such as the revised-Arrhenius model, the Johnson-Cook model, the revised Zerrili-Armstrong model and the intelligence algorithm ANN model [23]. The best correlation coefficient (\(R\)) in the work of [PERSON] et al. is 0.9989 at a high accuracy level; nevertheless, they only attempted a few parameter combinations of the three parameters (\(C\), \(\gamma\) and \(\zeta\)), and there is still room for improvement in accuracy and efficiency [23].