# A Deep Learning Method for the Prediction of Pollutant Emissions from Internal Combustion Engines
## 3 Developing and Optimization of the Artificial Neural Network
### Overview of the Procedures for Establishing the Structural Parameters of the Proposed Model
Specifically, the highest RMSE, observed in the prediction of CO for dynamic cycle 4 (Figure 9d), is 5.87%, while the lowest, at 1.57%, is observed in the prediction of HC for dynamic cycle 1 (Figure 9a). The results previously presented in Figure 9 are comprehensively summarized in Table 4.  
The prediction's regression accuracy (R\({}^{2}\)) performed by the optimal tested architecture, as shown in Figure 10, was determined using Equation (2):  
\[R^{2}=1-rMSE=1-\frac{MSE}{Var\big{(}Y_{target}\big{)}} \tag{2}\]  
where  
* \(rMSE\) is the relative mean squared error. * \(MSE\) is the mean squared error. Figure 9: BPANN prediction of the pollutant emission concentration for (**a**) dynamic cycle 1, (**b**) dynamic cycle 2, (**c**) dynamic cycle 3, (**d**) dynamic cycle 4, and (**e**) dynamic cycle 5. \(Var(Y_{target})\) refers to the variance of the random variable \(Y_{target}\). Variance is a statistical measure that represents the dispersion or spread of the values of \(Y_{target}\) around its mean. It quantifies how much the values of x deviate from the mean value \(\overline{Y}_{target}\). As is possible to observe, in all the charts, the data points are represented with predicted values plotted on the y-axis and target values on the x-axis. The closeness of the points to the diagonal dashed line reflects the accuracy of the predictions. Each graph is scaled according to the data range specific to each case. In accordance with the observations made in Figure 9 and Table 4, the BPANN demonstrates a consistent alignment along the interpolation line, with no significant deviations, for all pollutants analyzed across each dynamic cycle, thereby achieving exceptionally high accuracy. It is noteworthy that this architecture displays very little dispersion, with R\({}^{2}\) values becoming close to unity, definitely > 0.93, for all pollutants analyzed across each dynamic cycle: the highest R\({}^{2}\) value, 0.9871, is observed for HC emissions in dynamic cycle 1, while the only exception is the HC emission value in dynamic cycle 2, with an R\({}^{2}\) = 0.8814. The results previously presented in Figure 10 are comprehensively summarized in Table 5.  
Figure 10: BPANN regression prediction chart for (**a**) dynamic cycle 1, (**b**) dynamic cycle 2, (**c**) dynamic cycle 3, (**d**) dynamic cycle 4, and (**e**) dynamic cycle 5. The results highlight the robust learning abilities of the BPANN architecture, showcasing its effectiveness in accurately capturing and replicating the target trend throughout the training process. Nonetheless, certain uncertainties persist. The observed variability in RMSE values and the somewhat lower R\({}^{2}\) value of 0.8814 for HC in dynamic cycle 2 indicate that despite the BPANN's generally strong performance, there are factors affecting the accuracy of its predictions. These factors may include the model's sensitivity to specific operating conditions, the representativeness of the training data, and the inherent complexity of emission processes. To address these uncertainties, it is essential to improve data quality, refine the BPANN model, and perform sensitivity analyses to better understand and mitigate sources of prediction variability. Although the BPANN exhibits commendable performance, recognizing and addressing these uncertainties will be vital in enhancing its reliability in practical applications.