## 3 Results and Discussion
### ML Model Validation  
To evaluate the model's ability to adapt to new data and identify any issues, validation was carried out. The Root-Mean-Squared Error (RMSE) is derived from the square root of the Mean Squared Error (MSE) and offers an average measure of the absolute difference between predicted and actual values, where a lower RMSE signifies better performance. The developed model reached values of RMS = 18.37; RMS/Ym = 0.035; and MSE of 337.64. The R-squared (R\({}^{2}\)) metric was also employed to gauge how much of the variance in the target variable is explained by the model, reaching a value of 0.956 within a confidence interval of 95%. The methodology enhances precision and reliability in estimations, supporting robust conclusions and informed decision making prior to comparing it with the predicted sample CFD results shown in Table 2.  
The comparison between the machine learning model's predictions and the results from 3D CFD simulations offers a direct validation of the model's accuracy across multiple operational conditions. The low percentage error across all five cases indicates a strong agreement between the ML model's predictions and the CFD results, which are traditionally considered highly accurate but computationally expensive. The largest error is only 1.16% in Case 5, with other cases showing errors as low as 0.21% and even negative values, indicating \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Fuel [kg/s]** & **Air [kg/s]** & **Air [\({}^{\circ}\)C]** & **O\({}_{2}\) [\%]** & **Catalyst** & **ML** & **CFD** & **\% Error** \\ \hline Case 1 & 3.9392 \(\times\)\(10^{-5}\) & 7.203 \(\times\)\(10^{-4}\) & 675 & 10 & 33 & 575 & 577 & 0.34 \\ Case 2 & 1.57569 \(\times\)\(10^{-4}\) & 2.6508 \(\times\)\(10^{-4}\) & 685 & 5 & 32 & 461 & 460 & \(-\)0.54 \\ Case 3 & 3.9392 \(\times\)\(10^{-5}\) & 5.803 \(\times\)\(10^{-4}\) & 695 & 10 & 50 & 556 & 553 & 0.21 \\ Case 4 & 3.9392 \(\times\)\(10^{-5}\) & 2.5908 \(\times\)\(10^{-4}\) & 700 & 0 & 45 & 474 & 470 & 0.85 \\ Case 5 & 1.5757 \(\times\)\(10^{-4}\) & 3.901 \(\times\)\(10^{-4}\) & 724 & 0 & 50 & 511 & 517 & \(-\)1.16 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of machine learning model predictions compared to 3D CFD simulation results. Figure 6: Used multi-regression model for the machine learning process. slight over-prediction. This table demonstrates the reliability of the ML model for real-world application assessment, particularly in predicting fuel outlet temperatures under varying conditions of fuel flow rate, air flow rate, air temperature, oxygen content, and catalyst configuration. The minimal errors validate the feasibility of using the machine learning model once established as a design tool in place of more resource-intensive CFD simulations. The model's high accuracy makes it a viable option for screening and optimizing thermal management strategies in fuel reformers, reducing potential temperature gradients at the fuel cell stack inlet, and achieving process optimization with less computational overhead. In summary, the machine learning model provides a highly accurate, computationally efficient alternative to CFD simulations, as demonstrated by its predictive performance in Table 2. Its ability to handle varying input parameters and still maintain accuracy makes it a robust tool. Figure 7 depicts a demonstration of the ML model where two arbitrary but practice-relevant temperature values have been set as targeted outlet temperatures. The machine learning model predicts the ideal parameter configuration, taking into account the intricate, non-linear correlation between the assessed parameters and the fuel outlet temperature in the pre-reformer unit. Each variable's gradient indicates its impact level. Notably, the non-linear dynamics play a crucial role, evident when examining the air flow rate parameter.