# Predicting the Effect of Processing Parameters on Caliber-Rolled Mg Alloys through Machine Learning
## 3 Results and Discussion
[23] confirmed the microstructural evolution of MPCR-processed Mg alloy based on these stages. The expected and predicted microhardness values were arranged along the distance across the cross-section (Figure 5). The experimental data exhibited V-shaped variation, where the center exhibited low hardness and the two edges showed high values. These results were rationalized by the aforementioned inhomogeneity of \(\varepsilon_{eq}\) values, as shown in  
Figure 4: Variation in Vickers microhardness values depending on the number of applied MPCR deformation passes. Figure 3: FEA contour maps of \(\varepsilon_{eq}\) for AZ31 Mg alloy subjected to the eight-pass MPCR deformation: (**a**) on the cross-section and (**b**) on the lateral view. Figure 3a. Compared with the FEA results as well as the literature [18, 23, 32, 33], the actual hardness distribution was shifted towards the regime of higher distances. The hardness at the left edge of the cross-section (115 HV at a distance of 0 mm) was higher than that of the right edge (110 HV at a distance of 7.5 mm). In addition, the lowest hardness was confirmed not at the center but at the point pushed over towards the right edge (89 HV at a distance of 6 mm). Such a result arose from the imperfect rolling including the imbalance of lubrication and the disparity in rotation speed between the two rolls. This is also supported by the bent rod after the eight-pass MPCR deformation. The significant shear on the rod surface, as shown in Figure 3b, barely changed in spite of the imperfect rolling conditions. Therefore, the V-shaped variation in microhardness was maintained with the slight movement of the center. The predictability of machine learning was evaluated in three groups: the center, the left section, and the right section (Figure 6). The left and right sections indicate 25% distance from each edge. As shown in Figure 6a, the data were shown in the form of the root mean squared error (RMSE) for a quantitative analysis, expressed as:  
\[\text{RMSE}=\sqrt{\sum_{i=1}^{n}\frac{(y_{i}-\hat{y}_{i})^{2}}{n}} \tag{3}\]  
where \(n\) is the total number of data, \(y_{i}\) is the genuine datum, and \(\hat{y}_{i}\) is the predicted one. The ANN approach provided good predictability for the center area with a low RMSE of 3.03 HV. Integrating the GAN hardly enhanced the predictability with an RMSE of 2.98 HV. The ANN prediction for microhardness in the side sections was more difficult, as characterized by a significant increase in the RMSE to 7.33 HV for the left and 3.18 HV for the right. It should be noted that the GAN-aided ANN remarkably improved the predictability for this case. The RMSE was more than halved to 3.18 HV for the left side, although it was slightly increased to 4.76 HV for the right. Comparing the error rates of two models also provided a consistent conclusion, as shown in Figure 6b. The GAN-aided ANN model showed similar or lower error rates compared with the ANN in all experimental positions, except for the points at 2.5 and 7.5 mm. In particular, the GAN integration remarkably reduced the error rates from 10% to 5% at maximum in the left section. Figure 5: Line profile of Vickers microhardness values along the distance across the cross-section subjected to the eight-pass MPCR deformation. The data predicted by ANN and GAN-aided ANN approaches were also presented in the same format. The different effect of the GAN integration in relation to cross-sectional position can be understood in light of the shifted hardness distribution. The center area had a uniform distribution of hardness ranging from 91 to 99 HV. This condition was easy to predict for both approaches, resulting in the similarly low RMSE values. In contrast, the side sections were significantly more difficult to predict due to the shifted hardness distribution as well as the large hardness variation from 89 to 115 HV.