# Contributing towards Representative PM Data Coverage by Utilizing Artificial Neural Networks
## 3 Results and Discussion  
As aforementioned, the results presented in this section are for the AGP station. Descriptive statistics for the 2016-2018 period in the AGP monitoring station are presented in Table 2. This table includes yearly mean, max and min concentrations for each year individually and the corresponding values for the three years in total. Both PM\({}_{10}\) and PM\({}_{2.5}\) are measured in \(\mu\)g/m\({}^{3}\), and the monitoring methodology is based on beta radiation absorption. Table 3 includes the number of data points that were used for each subset during the development of the models (input data). There are more available data points for PM\({}_{10}\) due to the increased number of monitoring stations that were used as inputs. In both pollutant cases, when the meteorological parameters are added, they qualify as an additional predictor that has the same number of data points with the input stations' concentrations. Thus, the scenario with the most inputs, i.e., where both WS and T are incorporated, has a higher number of data points available for the training, validation and test subsets. In all cases, the architecture of the ANNs, following the experimental  
design of this work, defines the number of data points included in the input and output vectors. The size of the training-validation-test subset for the output vector is based on the 70-15-15 percentages which were introduced in the previous Section, and the resulting data points are 10,339-2215-2215 for PM\({}_{10}\) and 11,090-2376-2376 for PM\({}_{2.5}\). The data points of the output vector are the same for all four scenarios, as the output is always the PM concentrations at AGP. The architecture of the models is presented in Table 4. The number of inputs is the total number of predictor stations, and one (T, WS) or two meteorological parameters inputs (T and WS) are added according to the model used in the second, third and fourth row of the table. It is evident that the number of hidden neurons in the models for both PMs is lower when the meteorological data are not included in the inputs (16 and 13 hidden neurons for PM\({}_{10}\) and PM\({}_{2.5}\), respectively). The same number ranges from 26 to 30 for the remaining six schemes. This difference can be associated with the increased complexity of these networks. As more inputs with different characteristics are added to the network, the latter needs additional hidden neurons to simulate the relationship between input and target data. Tables 5 and 6 show the MAE, SD of MAE and \(R^{2}\) values for each of the eight models and the corresponding cases for the MLR method. These values are the result of applying the abovementioned metrics on the test subset of the output vector. When comparing the two methodologies, it is evident that the FFNN models outperform the MLR scheme for both PM\({}_{10}\) and PM\({}_{2.5}\) and all input scenarios. They display lower MAE and SD of MAE and higher R\({}^{2}\) values, indicating that the FFNNs methodology simulates more effectively the nonlinear relationship between the input and output parameters. Considering individually \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Input** & \
\begin{tabular}{c} **PM\({}_{10}\)** \\ **Hidden** \\ \end{tabular} & **Output** & **Input** &
\begin{tabular}{c} **PM\({}_{2.5}\)** \\ **Hidden** \\ \end{tabular} & **Output** \\ \hline PM & 8 & 16 & 1 & 5 & 13 & 1 \\ PM + T & 9 & 30 & 1 & 6 & 30 & 1 \\ PM + WS & 9 & 27 & 1 & 6 & 28 & 1 \\ PM + T + WS & 10 & 26 & 1 & 7 & 28 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of neurons in each layer of the models for PM\({}_{10}\) and PM\({}_{2.5}\) and the four different input cases.