## 3 Results
### Results of the Preliminary Data Analysis
#### 3.2.3 Results of Neural Network Training
Figure 14 shows the networks HL2-10-5 (Figure 14d); HL2-15-5 (Figure 14f) and HL2-15-10 (Figure 14g) required fewer iterations to training. Table 7 shows that the HL2-15-5 network is better than the others by all criteria except Q\({}_{2}\)-average relative error. The HL2-15-5 network is insignificantly inferior to the HL2-10-15 network in this criterion. At the same time, the HL2-10-15 network is inferior to other networks in many criteria. It is of interest to compare the training results of randomly selected neural networks and predefined neural networks. Table 8 and Figure 15 show the results of training and testing of eight selected neural networks with predefined number of synaptic coefficients: HL2-22-2 (Figure 15a); HL2-17-4 (Figure 15b); HL2-14-6 (Figure 15c); HL2-10-10 (Figure 15d); HL2-6-17 (Figure 15e); HL2-3-29 (Figure 15f); HL2-2-41 (Figure 15g); HL2-1-51 (Figure 15h). The network HL2-15-5 is close to the predefined networks HL2-17-4 and HL2-14-6 by number of neurons, precisely these two networks with the HL2-10-10 network that have Q\({}_{1}\) values less than one (see Table 8). The HL2-14-6 network has the lowest Q\({}_{2}\), Q\({}_{4}\) and Q\({}_{5}\) values (see Table 8). HL2-10-10 has the lowest Q\({}_{3}\), Q\({}_{6}\) values (see Table 8). In terms of the coefficient of determination, the network HL2-14-6 has one, which means 100% of the variance of the resultant quantity in the training set is explained by the influence of selected variables. Figure 15 shows that neural networks with a predefined number of neurons required significantly fewer iterations to train as compared to the brute-force selected networks. It is worth recalling again that Figures 14 and 15 show the best results from the number of multiple computational experiments. A smaller number of iterations was required to train the predefined neural networks. Having learnt the results of training two-layer networks, we noticed the following--the quality of neural network models is better if the number of neurons on the first layer is greater than on the second (Figures 14d-g and 15a-d). The results of training and testing two-layer neural networks are not entirely consistent with the observation in the case of single-layer neural networks. In the case of single layer neural networks, we observed the following--as the number of neurons on the hidden layer increases, the quality of neural network models becomes better. With two-layer networks, this is not true, e.g., HL2-22-2 with 24 neurons or HL2-17-4 with 21 neurons are in many ways (see Table 8) worse than the 20-neuron HL2-14-6 and HL2-10-10. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Neural Network** & **Q\({}_{1}\)** & **Q\({}_{2}\)** & **Q\({}_{3}\)** & **Q\({}_{4}\)** & **Q\({}_{5}\)** & **Q\({}_{6}\)** & **Q\({}_{7}\)** & **Q\({}_{8}\)** \\ \hline HL2-22-2 & 2 layers with 22 neurons on first layer and & & & & & & & \\  & 2 neurons on second layer & & & & & & & \\ HL2-17-4 & 2 layers with 17 neurons on first layer and & & & & & & & \\  & 4 neurons on second layer & & & & & & & \\ HL2-14-6 & 2 layers with 14 neurons on first layer and & & & & & & & \\  & 2 neurons on second layer & & & & & & & \\ HL2-10-10 & 2 layers with 10 neurons on first layer and & & & & & & & \\  & 10 neurons on second layer & & & & & & & \\  & 2 layers with 6 neurons on first layer and & & & & & & & \\  & 17 neurons on second layer & & & & & & & \\ HL2-3-29 & 2 layers with 3 neurons on first layer and & & & & & & & \\  & 29 neurons on second layer & & & & & & & \\  & 2 layers with 2 neurons on first layer and & & & & & & & \\  & 41 neurons on second layer & & & & & & & \\ HL2-151 & 2 layers with 1 neuron on first layer and & & & & & & & \\  & 51 neurons on second layer & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 8: Results of a trained predefined fully connected two-layer neural networks.