## 3 Results and Discussion
### Optimization and Benchmarks of ANN  
The primary tool used in this study to predict electricity production from panels was ANN. As mentioned in the Materials and Methods section, the GA was applied in this study to determine the best topology of the model (see Figure 3). The objective function for this procedure was the mean relative error of fitting between the ANN output and the measurement from the PVs. The relative error was selected, as it lets us adjust the actual differences by the size of the variable itself (see Section 2.2). The GA required 51 generations (steps of calculation) to reach the minimum with the desired accuracy (function tolerance of 1 \(\times\) 10\({}^{-2}\)). The progress of the GA is presented in Figure 3. As is noted, the penalty value shifted sharply during the procedure. The difference between best and worst in the selected generation reached above 30. However, the procedure stabilized in the last stage, after 43 generations, and  
Figure 3: The development of populations during the GA procedure. not improve the final score. The measured best, worst, and mean scores refer to all tested samples in the current generation and their objective function value. Based on the calculations presented above, the final GA recommendation was as follows: the best accuracy was provided by the cascade forward ANN structure. The optimization algorithm had a lower impact on the final solution, with few exceptions. The resilient backpropagation procedure was found to be the best in the sense of the obtained accuracy (MRE) of the model. As the performance function for ANN learning, the best results were registered for sum squared error (SSE). The recommended size of the ANN was two hidden layers and one output layer. The hidden layers had nine and six nodes, respectively. Since the genetic algorithm is a heuristic and fully arbitrary tool, the resulting recommendation is solely based on the adopted goal function (MRE). The obtained optimal solution, therefore, is based on purely numerical considerations and is not based on an analytical evaluation of individual parameters. The visualization of the system is presented in Figure 4.  
The distribution of available data between training, validation, and the test dataset was 82 to 6 to 12%. Splitting the data into subsets was a standard procedure to prevent false-positive model fits to experimental data. The higher size of test samples was found to be a good protection against overfitting. The results of the ANN training regression for the selected configuration were more than satisfactory. The overall R\({}^{2}\) value was 0.95, which indicates a very strong correlation. The best regression linearity (0.97) was achieved for the validation dataset--this can be explained by the fact that this subset was the smallest, so the result was in convergence with expectations. The lowest value was found for the test dataset (0.92). This set did not participate in the network's training, so by design this result was to be expected. Nevertheless, how little the linearity of this set deviates from the other two proves that we are not dealing with overfitting, which is particularly important in this kind of research. The training dataset was in the middle, just around the mean value (see Figure 5). The linearity indices obtained should be considered very high compared with related studies where the obtained R\({}^{2}\) values, depending on weather conditions, were very close to those presented here [55]. Figure 4: Visualization of the final ANN structure. To find the quantitative accuracy of the final model, as well as the GA objective function to distinguish it from ANN learning procedure objectives, the dataset from the last available 3 months was selected. Based on these data, a brief comparison between experimental and model values was performed. The final mean relative error (MRE) between the data set was 15.64%. The next comparison was intended to remove outliers.