## 5 Application
From Figure 12, it can be seen that the deformation of the specimen is inhomogeneous due to the friction between the specimen and anvils. The specimen can be broadly divided into hard deformation region, small deformation region and severe deformation region in accordance with deformation degree just as Figure 14. The friction between the specimen and anvils as well as constraint of anvils would significantly reduce the material flow abilities of the vicinity region of the end plane (region I in Figure 14), so this region is hard deformation region. The central region (region II in Figure 14) is slightly affected by the friction, meanwhile, the extrusion of the hard deformation region would greatly promote the material flow of this region, thus, large deformation would occur in the central region and it is defined as severe deformation region. As for the vicinity region of the cylindrical surface (region III in Figure 14), it is almost not affected  
Figure 11: The finite element model for the simulated isothermal compression tests of Inconel 718 superalloy. by the friction and the extrusion of other regions. The material in this region is roughly in a state of uniaxial compression, and its deformation degree is between the ones of hard deformation region and severe deformation region, so the vicinity region of the cylindrical surface is small deformation region. These simulation results are in good agreement with the real deformation circumstances of the isothermal compression tests. Besides, it could be clearly found from Figures 12 and 13 that the effective strains of the severe deformation regions under the conditions of 1153 K and 0.1 s\({}^{-1}\), 1303 K and 0.1 s\({}^{-1}\), 1153 K and 1 s\({}^{-1}\) and 1253 K and 1 s\({}^{-1}\) are all about 0.92, at the same time, the effective strain rates also reach the corresponding values of 0.1, 0.1, 1 and 1 s\({}^{-1}\) respectively, which indicate that the simulated process parameters can actually reflect the real experimental conditions. Corresponding to the simulation experiments above, the controlled simulation experiments using the FE model imported training stress-strain data of ANN in Section 3 were also conducted. Subsequently, the stroke-load curves data were exported from the FE solver. The continuously monitored stroke-load curves by the automatic data acquisition system in the compression tests were assumed to be the ideal curves. The comparisons among the simulated stroke-load curves using different FE models and the ideal curves were presented in Figure 15. From Figure 15, it was known that the simulated evolution rules of forming load with stroke are approximately in accordance with the experimental ones, indicating that the numerical simulation can indeed provide some guidance and reference for the practical processes. However, it is obvious that the predicted stroke-load curves with the FEM-implanted ANN model lie more close to the experimental curves from the global aspect. Especially when the stroke is above 3 mm, the simulated stroke-load curves with the training stress-strain data more and more diverge from the ideal curves, but the ones with the FEM-implanted ANN model can track the ideal curves in relatively high accuracy all along. The 10% error lines were given in Figure 15 as well, from which it was clearly seen that the errors of the predicted stroke-load curves with the FEM-implanted ANN model were always within 10% except the initial deformation stage (below 1 mm of deformation stroke), but the ones with the FEM imported training stress-strain  
\[y_{j}=\phi(net_{j})=\phi(\sum_{i=1}^{l}w_{ij}x_{i}+a_{j}) \tag{9}\]0 The effective strain distributions under the deformation conditions of (**a**) 1153 K and 0.1 s\({}^{-1}\); (**b**) 1303 K and 0.1 s\({}^{-1}\); (**c**) 1153 K and 1 s\({}^{-1}\) and (**d**) 1253 K and 1 s\({}^{-1}\). data cannot make it. It is valuable to note that, when the stroke is below 1 mm, all the simulation results appear relatively larger deviations from the ideal ones.