## 4 Conclusions  
This paper aimed at the development of a simulation tool for SOFC performances based on a feed-forward backpropagation neural network algorithm. The neural network approach was chosen  
Figure 6: ANN5 application: comparison of simulated and experimental polarization curves (**a**) under Exp synF and (**b**) Exp synG operating conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{
\begin{tabular}{c} **Exp synF** \\ **Settings** \\ \end{tabular} } & \multicolumn{2}{c}{**Exp synG**} & \multicolumn{2}{c}{**ANN5**} \\  & & **Settings** & & **Input Range** \\  & & & **Min** & **Max** \\ \hline Temperature (\({}^{\circ}\)C) & & 765 & 800 & 700 & 800 \\ \hline Equivalent hydrogen flowrate & \multirow{3}{*}{18.34} & \multirow{3}{*}{15.48} & \multirow{3}{*}{10.80} & \multirow{3}{*}{23.56} \\ (mL\(\cdot\)min\({}^{-1}\cdot\)cm\({}^{-2}\)) & & & & & \\ \cline{3-5}  & H\({}_{2}\) & 3.67 & (20.0\%vol) & 5.16 & (20.0\%vol) & 0 & 10.51 \\ \cline{3-5}  & CO & 7.34 & (40.0\%vol) & 5.16 & (20.0\%vol) & 0 & 12.74 \\ \cline{3-5} Area Specific partial flowrates & CO\({}_{2}\) & 2.75 & (15.0\%vol) & 3.87 & (15.0\%vol) & 0 & 5.73 \\ (mL\(\cdot\)min\({}^{-1}\cdot\)cm\({}^{-2}\)) & CH\({}_{4}\) & 1.83 & (10.0\%vol) & 1.29 & (5.0\%vol) & 1.27 & 11.46 \\ \cline{3-5}  & N\({}_{2}\) & 2.75 & (15.0\%vol) & 10.32 & (40.0\%vol) & 0 & 32.17 \\ \hline Current density (mA\(\cdot\)cm\({}^{-2}\)) & & 0–500 & & 0–500 & 0 & 1300 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Validation experiments input data. in order to get a lean and quick simulator that can be implemented in any computational code/system simulation software, without getting computational time slower because of the complexity due to a deterministic set of detailed modelling equations. As a result, a 3-hidden layer network (featuring 25, 22 and 18 neurons and a transfer function Tansig) is the best configuration to fit the experimental data collected for the purpose, by means of thorough test campaign on state-of-the-art SOFC materials. The accuracy of the developed model is very high, implying low forecast errors in reproducing SOFC output voltage fed with fuels with a variable hydrogen concentration, as well as variable amount of non-reformed light hydrocarbons (in this study, methane was considered as model compound for this category). Furthermore, the variation of the fuel utilization, as well as the operating temperature of the cell, are considered to build the application framework of the model. The last two features make this neural network simulator advanced with respect to other already presented and provide the additional value when it comes to SOFC operation in integrated systems. In detail, considering the error between experimental results and data-set used for the development, \(RMS\) on forecast is 0.67%, while it is slightly higher 2% and 3% respectively in the simulation of a polarization curve obtained in a different experiment with the same SOFC type and in reproducing the performance of a SOFC cell with different geometry. However, \(RMS\) shrinks to about 1%, whether the typical current density range for SOFC operation (300-500 mA\(\cdot\)cm\({}^{-2}\)) is observed. For the features of the experimental data-set used as training basis and the interpolation capability of the algorithm verified through the final validation data-set, the model can be applied whether the SOFC operating variables fall into the neural network input range.