## 5 Results and Discussion  
The offered MLP-ANN approach utilized the log-sigmoid transfer function (logsig) and linear transfer function (purelin) in its hidden and output layers, respectively. The aim was to optimize the hidden layer neurons. This was done using trial and error. Twelve neurons were optimally available in the hidden layer of the MLP-ANN tool. Figure 2 illustrates the MLP-ANN model's performance when using the training data over several iterations. The MLP-ANN was trained using the Levenberg-Marquardt (LM) algorithm. Table S2 shows the optimal values of the MLP-ANN structure. Moreover, in the hidden layers of the RBF-ANN model, the RBF was used. Based on previous results, for the ANN, the number of hidden layer neurons is chosen to be less than one-tenth of the total number of training data points [82]. Ergo, it was assumed that the number of hidden layers of this algorithm was one-tenth of the total number of data points used for training. Figure 3 shows the LM algorithm based on the MSE of various iterations for the RBF-ANN. In Figure S1, the obtained membership functions are shown for the ANFIS model. This figure emphasizes that all of the data (output and input) were normalized in the range \([-1,\,1]\). Figure 4 demonstrates the RMSE of the actual \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & **Abbreviation** & \
\begin{tabular}{c} **Temperature** \\ **(°C)** \\ \end{tabular} &
\begin{tabular}{c} **Nanoparticle Type** \\ **and Concentration** \\ **(vol\%)** \\ \end{tabular} & **No. of Data** \\ \hline
1-butyl-3-methylimidazol & & & & & \\ bis(trifluoromethylsulfonyl)imide & & & & & \\
1-butyl-2,3-dimethylimidazol & & & & & \\ bis(trifluoromethylsulfonyl)imide & & & & & \\ \hline N-butyl-N-methylpyrrolidin & & & & & \\ bis(trifluoromethylsulfonyl)imide & & & & & \\ N-butyl-N,N,N-trimethylammonium & & & & & \\ bis(trifluoromethylomethsulfonyl)imide & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The list of ionic liquids (ILs) studied in the literature for the prediction of \(C_{p}\). and estimated \(C_{p}\) values for the training data. The highest number of iterations was 1000, and the best RMSE was 0.17416. Figure 3: The performance of the LM algorithm according to the MSE of different iterations for the radial basis function (RBF)–ANN. Figure 2: The performance of the Levenberg–Marquardt (LM) algorithm according to the mean squared error (MSE) of different iterations for the multilayer perceptron–artificial neural network (MLP–ANN). To create the structure of the SGB, the different parameters of this algorithm needed to be determined. These parameters were the number of additive terms, learning rates, minimum \(n\) in the child node, and the proportion of the sub-dataset. Table 2 gives details of the trained models. Figure S2 shows the predicted and actual (experimental) values of the \(C_{p}\)s, which were obtained with different models. Figure 5 illustrates the regression diagrams of four models for the computed and actual values. According to these figures, both the training and testing results showed a surprisingly good fit to a straight line for the SGB model; however, the obtained fits for the other models did not give benchmarking results compared to the SGB. The MLP-ANN algorithm seems to have produced estimations than the ANFIS and RBF-ANN algorithms. The \(R^{2}\) coefficient of the SGB method was 0.994 for both the training and testing datasets. The \(R^{2}\) values were 0.933 and 0.943, 0.8499 and 0.8754, and 0.9327 and 0.9204 for the training and testing datasets of the MLP-ANN, ANFIS, and RBF-ANN algorithms, respectively.