# Intelligent Prediction of Nitro Oxide Capture in Designable Ionic Liquids
## 4 Results and Discussion
### Solubility Prediction of N\({}_{2}\)O in Ionic Liquids via TLFFNN Method  
The accuracy of the model trained using the TLFFNN method on test sets is presented in Table 7. As the table shows, the models exhibited superior performance. For example, for [BMIM][Tf\({}_{2}\)N], it had a very low MSE value of 5.06 \(\times\) 10\({}^{-6}\) and a very high R\({}^{2}\) value of 0.9996. In the case of [DMIM][MP], the values of MSE and R\({}^{2}\) were 3.46 \(\times\) 10\({}^{-5}\) and 0.9978, respectively. The averaged metrics for the training sets, test sets and all datasets are also shown in Table 6. The averaged values of MSE, RMSE, and R\({}^{2}\) were 2.37 \(\times\) 10\({}^{-5}\), 4.23 \(\times\) 10\({}^{-3}\), and 0.9984, respectively, which were superior values. We showed that the model trained using the TLFFNN method could accurately predict N\({}_{2}\)O solubility in all the ionic liquids involved in this study, even with a very limited dataset. It was the most accurate method used in this research.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Ionic Liquid** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline
1 & [BMIM][BF\({}_{4}\)] & 2.447 \(\times\) 10\({}^{-5}\) & 4.946 \(\times\) 10\({}^{-3}\) & 0.9988 \\
2 & [BMIM][AC] & 6.109 \(\times\) 10\({}^{-6}\) & 2.472 \(\times\) 10\({}^{-3}\) & 0.9988 \\
3 & [BMIM][Tf\({}_{2}\)N] & 5.055 \(\times\) 10\({}^{-6}\) & 2.248 \(\times\) 10\({}^{-3}\) & 0.9996 \\
4 & [BMIM][SCN] & 3.366 \(\times\) 10\({}^{-5}\) & 5.801 \(\times\) 10\({}^{-3}\) & 0.9944 \\
5 & [DMIM][MP] & 3.460 \(\times\) 10\({}^{-5}\) & 5.882 \(\times\) 10\({}^{-3}\) & 0.9978 \\
6 & [(ETO)\({}_{2}\)IM][Tf\({}_{2}\)N] & 3.107 \(\times\) 10\({}^{-5}\) & 5.574 \(\times\) 10\({}^{-3}\) & 0.9990 \\
7 & [(OH)\({}_{2}\)IM][Tf\({}_{2}\)N] & 2.381 \(\times\) 10\({}^{-5}\) & 4.880 \(\times\) 10\({}^{-3}\) & 0.9984 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Performance of models via the TLFFNN method.  
Figure 6: Plots for predicted solubility with experimental values via the voting method. (**a**) N\({}_{2}\)O in [BMIM][Tf\({}_{2}\)N] during training; (**b**) N\({}_{2}\)O in [BMIM][Tf\({}_{2}\)N] during testing; (**c**) N\({}_{2}\)O in [(ETO)\({}_{2}\)IM][Tf\({}_{2}\)N] during training; and (**d**) N\({}_{2}\)O in [(ETO)\({}_{2}\)IM][Tf\({}_{2}\)N] during testing.  
Comparisons of predicted solubility and experimental values are plotted in Figure 7, consisting of two ionic liquids, [(ETO)2 IM][Tf2N] and [BMIM][Tf2N]. The laboratory value and forecast solubility were very consistent for both the training and testing stages. This visual evaluation clearly highlights the models' outstanding accuracy and reliability levels. By adjusting the weights and biases, the TLFFNN method could effectively overcome the problem of insufficient datasets. It could also be used to forecast how soluble N2O would be in ionic liquids.  
The discrepancy between the outputs and the objectives is visualized in the error histogram. Figure 8 shows the error between the model predictions and experimental values of N2O solubility in [BMIM][Tf2N] via the TLFFNN method. The abscissa \"Errors\" represents the D-value of experimental values and predictions; the ordinate represents the  
Figure 7: Plots for predicted solubility with experimental values via the TLFFNN method. (**a**) N2O in [BMIM][Tf2N] during training; (**b**) N2O in [BMIM][Tf2N] during testing; (**c**) N2O in [(ETO)2 IM][Tf2N] during training; and (**d**) N2O in [(ETO)2 IM][Tf2N] during testing.  
number of instances with corresponding errors. As shown in Figure 8, the errors were very small. In the histogram, most instances are gathered near the zero error line, and the histogram is distributed normally around the zero-error line. This error histogram proves that the TLFFNN model was highly coordinated with experimental values in determining how soluble N2O would be in various ionic liquids.