## 3 Results and Discussion
### Extreme Learning Method  
Compared with the traditional NN method, the Extreme Learning Method (ELM) uses a single-layer forward NN method, which allows the ELM to avoid training the input layer, only training the output for improved training velocity while maintaining the general performance of the developed model.  
Researchers utilize the advantage of the fast training velocity of the ELM, which bypasses iterative optimization methods such as gradient descent, for developing CO\({}_{2}\)/NO\({}_{\mathrm{x}}\) emissions from power plants with high computational efficiency. In the study of [48], the authors used the ELM to model and optimize NO\({}_{\mathrm{x}}\) emissions with real data from CEM in a coal-fired power plant. The new proposed ELM demonstrated good generalization compared to the widely used NN and SVM by examining the relationship between the NO\({}_{\mathrm{x}}\) emissions and the operational parameters in the model. It was found that the MRE from the ELM was 1.13%, which was better than the NN and the SVM. This is an exemplary study that shows that the ELM-based machine learning models can not only predict NO\({}_{\mathrm{x}}\) emissions but also have the potential to serve as an alternative and effective approach to optimize the operational parameters of the fossil fuel power plant (e.g., gas flowrates, temperature, and pressure, out of a total of six selected parameters) to reduce NO\({}_{\mathrm{x}}\) emissions. Using similar techniques, Ref. [49] constructed a bootstrap aggregated ELM model comprising multiple ELM models, which were created through bootstrap re-sampling replication of the original training data to forecast the CO2 capture rate and level. By utilizing the mean square error of the prediction results from various hidden neurons as a comparison metric, the bootstrap aggregated ELM model outperformed a single ELM model in delivering more precise and dependable predictions along with model prediction confidence intervals. The authors of Ref. [50] further improved the controlling and monitoring system of the combustion furnace by using ELM and NN algorithms in machine learning. It is revealed that the ELM outperformed the NN as it required less training time and exhibited lower average errors.  
The authors of Ref. [48] introduced a NOx prediction model utilizing an ELM algorithm for coal-fired boilers at a power station. This model was subsequently employed to enhance operations for the reduction of NOx emissions. The ELM algorithm is characterized as a single hidden layer feedforward neural network. The development of the model was based on ten days of operational data. The NOx emissions forecasted by the model exhibited a good match with the actual NOx values in terms of mean absolute error (MAE) and had an R-value of 98%. Furthermore, Ref. [51] compared the model's accuracy with different machine learning algorithms, and it was found that the ELM has superior performance in terms of prediction accuracy and computational time.  
Although the ELM is very popular among researchers for developing a computationally efficient machine learning model for CO2/NOx emissions, as we discussed above, one needs to note that attention needs to be paid to the overfitting issue inherited by the ELM. In addition, the ELM is characterized by its opaque nature, which presents challenges in areas where clarity and understanding are essential, which is especially important for the carbon emission evaluation process.  
Table 2 shows a summary of the applications of machine learning methods in CO2/NOx emission evaluation. Forward neural networks and Extreme learning methods seem to be better when addressing the real-time prediction of CO2/NOx emissions due to their computational efficiency.