# Intelligent Prediction of Nitro Oxide Capture in Designable Ionic Liquids
## 4 Results and Discussion
### Solubility Prediction of \(N_{2}o\) in Ionic Liquids via the Linear Regression Method  
A linear function could be fitted for each N\({}_{2}\)O\(-\)IL system after training using the linear regression method; this empirical correlation, which is expressed in Equation (2), has six coefficients. The coefficients for Equation (2) are presented in Table 3.  
The proposed function was also evaluated for each N\({}_{2}\)O\(-\)IL system; the metrics during the testing stages are shown in Table 4. As can be seen, this model is accurate in predicting the solubility of N\({}_{2}\)O in some kinds of ionic liquids, such as [BMIM][Tf\({}_{2}\)N]; it had an MSE of 6.770 \(\times\) 10\({}^{-4}\), an RMSE of 2.602 \(\times\) 10\({}^{-2}\), an MAE of 2.296 \(\times\) 10\({}^{-2}\), and an R\({}^{2}\) of 0.9541; this performance was determined to be acceptable. However, for some ionic liquids, the result was not satisfactory, such as for [(ETO)\({}_{2}\)IM][Tf\({}_{2}\)N]; the model had an MSE of 1.303 \(\times\) 10\({}^{-2}\), an RMSE of 1.142 \(\times\) 10\({}^{-1}\), an MAE of 8.233 \(\times\) 10\({}^{-2}\), and an R\({}^{2}\) of 0.3349. The average metrics for the training sets, test sets, and all datasets are shown in the following section; the overall MSE, RMSE, MAE, and R\({}^{2}\) were 3.397 \(\times\) 10\({}^{-3}\), 5.017 \(\times\) 10\({}^{-2}\), 3.934 \(\times\) 10\({}^{-2}\), and 0.7924, respectively. Overall, the linear regression method was shown to be weak in predicting N\({}_{2}\)O solubility. Figure 4: The learning loss curve of modeling (**a**) N\({}_{2}\)O in ionic liquid [(ETO)\({}_{2}\)IM][Tf\({}_{2}\)N] via the linear regression method, (**b**) N\({}_{2}\)O in ionic liquid [BMIM][AC] via the voting method, (**c**) and N\({}_{2}\)O in ionic liquid [BMIM][Tf\({}_{2}\)N] via the two\(-\)layer feed\(-\)forward neural network. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**No.** & **Ionic Liquid** & \(\theta_{0}\) & \(\theta_{1}\) & \(\theta_{2}\) & \(\theta_{3}\) & \(\theta_{4}\) & \(\theta_{5}\) \\ \hline
1 & [BMIM][BF\({}_{4}\)] & 0.6233 & \(-\)0.0021 & 0.0048 & 0.0001 & 0.0000 & 0.0000 \\
2 & [BMIM][AC] & 0.2340 & \(-\)0.0007 & 0.0735 & 0.0000 & 0.0000 & 0.0000 \\
3 & [BMIM][Tf\({}_{2}\)N] & 0.5342 & \(-\)0.0017 & 0.0224 & 0.0000 & 0.0000 & 0.0000 \\
4 & [BMIM][SCN] & 0.7933 & \(-\)0.0014 & 0.0022 & \(-\)0.0003 & 0.0000 & 0.0000 \\
5 & [BMIM][MP] & 0.8816 & \(-\)0.0027 & 0.0027 & 0.0000 & 0.0000 & 0.0000 \\
6 & [(ETO)\({}_{2}\)IM][Tf\({}_{2}\)N] & 1.287 & \(-\)0.0032 & 0.0038 & 0.0000 & 0.0000 & 0.0000 \\
7 & [(OH)\({}_{2}\)IM][Tf2N] & 1.050 & \(-\)0.0026 & 0.0024 & 0.0000 & 0.0000 & 0.0000 \\ \hline \end{tabular}
\end{table} 
Table 3: The coefficients fitted for Equation (2) via the linear regression method. In order to better understand the model, cross plots are presented in Figure 5. We took two ionic liquids as examples, and for both training and testing rounds, the predicted solubility of N2O was contrasted with the experimental data. As illustrated in Figure 5, most predicted data were similar to the experimental data. However, significant deviations were identified in both training and testing phases, which indicates the weak ability of the linear regression model in N2O solubility prediction. This result could have been due to the limited number of datasets for N2O solubility; only a few dozen can be collected from the available literature for most kinds of ionic liquids.