# A Deep Learning Method for the Prediction of Pollutant Emissions from Internal Combustion Engines
## 1 Introduction  
To address the critical need for reducing air pollution from vehicles and improving air purity, increasingly stringent guidelines on pollutants and greenhouse g  
leading to extended operating times and higher costs. Furthermore, their performance progressively declines over time due to challenging conditions [18]. Sophisticated technologies, including machine learning (ML) methodology [19], are currently under investigation to efficiently track the parameters of the SI engine, with the aim of addressing the aforementioned challenges. The improvement of engine design depends on attaining optimal efficiency, which is essential in boosting engine performance while concurrently minimizing fuel consumption and reducing pollutant emissions [20; 21]. Incorporating advanced technologies such as machine learning can enhance this optimization process. The ability of ML models to examine sophisticated dataset structures derived from input data renders them particularly suitable in predicting pollutant emissions in internal combustion engines. Data-driven approaches can enhance combustion strategies, leading to improved efficiency and lower emissions [22; 23]. However, the direct on-board implementation of these measurements using physical instruments is challenging. Therefore, preliminary characterizations on specific test benches are necessary for proper engine calibration. [PERSON] et al. [24] proposed the modeling of \(\mathrm{NO_{x}}\) and HC raw emissions in a six-cylinder gasoline engine that operates under highly transient conditions with the utilization of machine learning approaches. The regression accuracy metric (R\({}^{2}\)) for the optimal model predicting \(\mathrm{NO_{x}}\) is 0.98 for the training data and 0.97 for the test data. In contrast, the best model for predicting HC achieves values of 0.90 for the training data and 0.89 for the test data. [PERSON] et al. [25] proposed models based on artificial neural networks (ANNs) for estimating \(\mathrm{NO_{x}}\) and \(\mathrm{CO_{2}}\) emissions from the in-cylinder pressure of a maritime diesel engine. The models utilize the Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) network architectures. The results demonstrate that the MLP model exhibits greater accuracy, with a low mean average percentage error (MAPE), in estimating both \(\mathrm{NO_{x}}\) (MAPE = 4.39%) and \(\mathrm{CO_{2}}\) (MAPE = 1.08%) compared to the RBF network (MAPE = 11.8% for \(\mathrm{NO_{x}}\) prediction and MAPE = 14.2% for \(\mathrm{CO_{2}}\) prediction). [PERSON] et al. [26] demonstrated the use of machine learning techniques to predict combustion, performance, and emission parameters in a dual-fuel SI engine operating on neat gasoline and E20 ethanol. While the ANN model exhibited reliable performance and accuracy, the ensemble least-squares boosting (ELSB) technique achieved an even higher degree of agreement with the experimental data. [PERSON] et al. [27] developed a back propagation (BP) neural network model to predict ignition delays for three-component surrogates using the pressure, ambient temperature, and molar fractions of n-heptane, iso-octane, and toluene as inputs. Their model, trained with data from single- and two-component surrogates, successfully predicted ignition delays for Toluene Primary Reference Fuel (TPRF) surrogates. The neural network composed of two hidden layers outperformed one with a single layer, and optimization improved accuracy with a correlation coefficient above 0.9996. The model also significantly reduced the computation time and accurately predicted the Motor Octane Number (MON) and Research Octane Number (RON). It enabled the precise matching of real fuels to surrogate advanced combustion engines. [PERSON] et al. [28] introduced a hybrid algorithm called physics-aware training that enables the use of backpropagation to train physical systems in situ.