## 3 Results
### Performance Comparison of the Unseen Test Set  
In order to test the model's ability to adapt properly to new or images of arbitrary size to support the requirements of the domain experts and real applications, 59 original images provided by the experts were used in this experiment. More specifically, two experiments were conducted on the additional unseen test set: (1) in the first experiment, the original image with a size of about 100 \(\times\) 100 was directly used as the input for the developed models; (2) in the second experiment, before the test was conducted, we followed a similar mixing procedure to generate an image as the input for the model that is the same size as the training data (400 \(\times\) 400) but comes from the same source image. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Backbone**} & \multicolumn{6}{c}{**W/O Pre-Trained**} & \multicolumn{6}{c}{**W/Pre-Trained**} \\ \cline{2-11}  & \multicolumn{3}{c}{**MAE**} & \multicolumn{3}{c}{**MAEB**} & \multicolumn{3}{c}{**MAE**} & \multicolumn{3}{c}{**MAEB**} \\ \cline{2-11}  & **S** & **M** & **1** & **S** & **M** & **1** & **S** & **M** & **I** & **S** & **M** & **I** \\ \hline AlexNet & 15.2 & 20.4 & \(-\)5.2 & 13.3 & 13.4 & \(-\)0.02 & 10.2 & 15.1 & \(-\)4.9 & 11.3 & 11.66 & \(-\)0.34 \\ VGG-16 & 16.4 & **7.8** & **+8.6** & 13.2 & 11.2 & \(+\)2 & 9.3 & **7.6** & **+1.7** & **6.54** & **5.92** & \(+\)0.62 \\ ResNet-18 & **10.2** & 9.3 & +0.9 & **11.6** & 11.6 & +0.06 & **8.1** & 7.8 & +0.3 & 11.6 & 11.64 & 0 \\ SqueezeNet & 11.8 & 10.7 & +1.1 & 13.6 & 10.6 & **+3.06** & 8.5 & 8.1 & +0.4 & 9.94 & 7.26 & +2.68 \\ GoogLeNet & 9.5 & 9.3 & +0.2 & 11.7 & **10.5** & +12.2 & **8.1** & 7.9 & +0.2 & 12.4 & 9.32 & **+3.08** \\ \hline \hline \end{tabular}  
* The bold highlight is the best-performed configuration. The best MAE and MAEB are underlined.  
\end{table} 
Table 2: Performance comparison between the baseline (single-task, abbreviated as S) and the proposed multitask learning models (abbreviated as M) on the synthesized test set. The column “I” indicates the improvement achieved by applying multi-task learning. The results for the first and second experiments are shown in Tables 3 and 4, respectively. Indeed, the best MAE and MAEB were achieved by the model initialized with the pre-trained parameters. Among them, the model with GoogLeNet backbone achieved the best MAE if the original image was used, while the model with VGG as a backbone generally outperformed the others in terms of both MAE and MAEB. Furthermore, considering both the results shown in this and previous subsections, we can observe that the proposed model with multi-task learning indeed reduces regression errors, regardless of whether the test is conducted by using mixed images or original images. However, comparing the experimental results shown in Table 4 with Table 3 illustrates that the regression errors for the original images are higher than those of the mixed images. We believe that is for the following reasons: the first is that, during our training process, all the developed models were  
of the proposed multi-task learning architecture on one material; while it has potential beneficial effects on other materials, we did not have the opportunity to collect data and conduct experiments to highlight the potential benefits. The mechanical properties in steels are strongly governed by the presented microstructures. In our study, several factors--the mechanical properties of the particular material, mixture microstructure, and grain size--are required for further discussion. For microhardness in different studied microstructures, steels with pearlite, bainite, and martensite microstructures were cold-rolled to maximum equivalent strains of 3.0, 2.5, and 2.0, respectively [33]. The hardness evolution as a function of the equivalent von Mises strain for the above microstructures is shown to be 300-500 HV for pearlite, 450-700 HV for banite, and 700-1000 HV for martensite [33]. Mixed microstructures combined particular properties.