## 3 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**MLP 4-7-1**} \\ \hline
**Regression Statistics** & **T for Training File** & **T for Validation File** & **T for Testing File** \\ \hline Data Mean & 37.8574 & 37.9499 & 37.4636 \\ Data S.D. & 4.8059 & 5.0527 & 4.9947 \\ Error Mean & \(-0.0002\) & \(-0.0120\) & \(-0.0181\) \\ Error S.D. & 0.2605 & 0.2780 & 0.2806 \\ Abs Mean & 0.1923 & 0.2107 & 0.2082 \\ S.D. Ratio & 0.0542 & 0.0550 & 0.0562 \\ Correlation & 0.9985 & 0.9985 & 0.9984 \\ \hline \hline \multicolumn{3}{c}{**MLP 4-10-1.**} \\ \hline
**Regression Statistics** & **T for Training File** & **T for Validation File** & **T for Testing File** \\ \hline Data Mean & 37.6776 & 38.0241 & 37.7491 \\ Data S.D. & 5.0388 & 4.7779 & 4.8083 \\ Error Mean & 0 & 0.0040 & \(-0.0058\) \\ Error S.D. & 0.1438 & 0.1627 & 0.1579 \\ Abs Mean & 0.1046 & 0.1079 & 0.1073 \\ S.D. Ratio & 0.0285 & 0.0341 & 0.0328 \\ Correlation & 0.9996 & 0.9994 & 0.9995 \\ \hline \hline \multicolumn{3}{c}{**MLP 4-5-1.**} \\ \hline
**Regression Statistics** & **T for Training File** & **T For Validation File** & **T for Testing File** \\ \hline Data Mean & 37.9323 & 37.7615 & 37.5023 \\ Data S.D. & 4.8752 & 4.6902 & 5.2108 \\ Error Mean & 0 & 0.098 & 0.0197 \\ Error S.D. & 0.4326 & 0.4466 & 0.4554 \\ Abs Mean & 0.3445 & 0.3454 & 0.3557 \\ S.D. Ratio & 0.0887 & 0.0952 & 0.0874 \\ Correlation & 0.9961 & 0.9955 & 0.9962 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Regressive statistics both for the selected model and the rejected models, for training set, validation set and testing set, respectively. * Correlation--the standard Pearson R correlation coefficient for the values required and obtained at the output. The two final indicators presented in Table 3, namely, the ratio of standard deviations and correlation, were essential for evaluating the predictive capacity of the developed neural network. The lower the ratio of the standard deviations (closer to zero) and the higher the correlation (closer to one), the better the network. Table 3 shows that the correlation was about 0.998, which was a close approximate for the files: training, validation and testing, although the ratio of the standard deviations for the errors and for the data was in the 0.05 range. The indicative visualization of the neural network operations that were generated was a 2-dimensional function, referred to as the network response area. For variables Z and t (at the defined X = 0.5 and Y = 0.5), the response surface of the MLP 4-7-1 network is shown in Figure 6. Undoubtedly, the visualization of the temperature distribution in the rock bed heat storage during the stagnation phase, based on this neural model, more fully represented the heat flow caused mainly by free convection. In the case of the generated surface, with all the assumed principles (at the defined X = 0.5 and Y = 0.5), by MLP 4-10-1 network, we can observe some disturbances in the layout, namely the occurrence of two temperature maximums at the end of the storage process (see Figure 7). Such a temperature layout has no physical grounds and was the reason this neural model was rejected. In the opinion of the authors, this was the effect of network's over-learning. Figure 4: The results of linear regression for the temperature values in deposit measured using Celsius scale and determined using the MLP 4-7-1 model in relation to the testing file (of data). Figure 5: The results of absolute error for the temperature values determined using the MLP 4-7-1 model in relation to the testing file. Figure 6: Temperature distribution in dimensionless function of deposit height and time for definite dimensionless value X = 0 and Y = 0 (according to Figure 2) obtained from the model MLP 4-7-1 network. Figure 7: Temperature distribution in dimensionless function of deposit height and time for definite dimensionless values X = 0 and Y = 0 (according to Figure 3) obtained from the model MLP 4-10-1 network.