## 3 Results
### Constructing the Architecture of Neural Networks and Their Training  
To describe changes in the average grain diameter \(D\), the fraction of low-angle boundaries \(P_{L}\), and the density of low-angle boundaries \(S_{L}\) during deformation at temperatures between 300 and 500 \({}^{\circ}\)C, three neural networks with a general scheme (multilayer perceptron) were constructed (Figure 4). The neural networks were trained according to the experimental data from Table 3. Verification was performed according to the experimental data from Table 4, which were obtained at temperatures and strain rates different from those used for training. The images of the microstructures obtained with the thermomechanical deformation parameters from Table 4 are shown in Figure 12.  
As it was shown in Section 3.1, the average grain diameter, and the fraction and density of low-angle boundaries vary nonmonotonically. Therefore, in order to take into account correctly the nonmonotonicity of the relations of the microstructure parameters to the thermomechanical parameters of deformation, which have a form similar to those shown in Figures 9-11, it is necessary to use a large number of neurons (usually more than 20). It should be borne in mind that the number of weight coefficients that need to be determined by training significantly exceeds the number of neurons in the hidden layer. If we choose a neural network structure with one hidden layer and three input neurons (Figure 4), the number of the weight coefficients of the neural network is four times the number of neurons in the hidden layer. In this study, 36 sets of experimental data relating the average grain diameter to temperature, strain, and strain rate were obtained. Similar sets were obtained for the fraction and density of low-angle boundaries. Thus, the maximum number of possible neurons in the hidden layer with such a single-layer neural network is nine. A neural network with this number of neurons makes it possible to describe the evolution of the average grain diameter depending on the thermomechanical parameters of deformation with an average relative deviation of 11%. The average relative deviation for each investigated microstructure parameter is calculated using the formula  
\[\delta=\frac{1}{N}\sum_{i=1}^{N}\frac{\left|\varphi_{i}-z_{i}\right|}{z_{i}} \cdot 100\% \tag{2}\]  
where \(\varphi_{i}\) and \(z_{i}\) are the calculated and experimental values of the compared values obtained under the same conditions (in this paper, these values are the average grain diameter \(D\) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Temp\({}_{\
u}\)**, \({}^{\circ}\)C** & & **350** & & & **450** & \\ \hline Strain & 0.10 & 0.35 & 0.54 & 0.08 & 0.34 & 0.54 \\ Strain rate, \(s^{-1}\) & 0.30 & 1.14 & 1.75 & 0.30 & 1.20 & 1.90 \\ \(D\), \(\mu\)m & 4.41 & 3.02 & 2.19 & 4.71 & 3.58 & 2.67 \\ \(P_{L}\) & 0.59 & 0.80 & 0.64 & 0.44 & 0.64 & 0.54 \\ \(S_{L}\), \(\mu\)m\({}^{-1}\) & 0.06 & 0.18 & 0.23 & 0.03 & 0.15 & 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Microstructure parameters of the AlMg6/10 % SiC MMC at temperatures of 350 and 450 \({}^{\circ}\)C.  
and the fraction \(P_{L}\) and density \(S_{L}\) of low-angle boundaries); and \(N\) is the total number of compared values. To increase the number of hidden neurons in the neural network, it is necessary to increase the size of the sample by which the neural network is trained. Augmentation is one of the possible ways of increasing the sample size by which the neural network is trained. The essence of this method is experimental data noising. Certainly, this method sometimes allows the problem of neural network uncertainty to be solved. However, as computational experiments have shown, it is impossible to achieve a significant reduction in the average relative deviation for the dependences obtained in this study. As a result, a method of processing experimental data was proposed, which consists of approximating experimental data using a surface, followed by adding data to the training sample.