# Machine-Learning Model Prediction of Ionic Liquids Melting Points
## 3 Results
### Deep-Learning (DL) Model Performance  
To quantify the accuracy of the prediction from the deep-learning (DL) model we described in Sect. 2, the model performance was assessed based on two metrics such as the square coefficient of correlation (\(R^{2}\)), and the root mean square error (RMSE), which estimates statistical accuracies in the predictions. A summary of the model's performance is presented in Table 1. The performance metrics (e.g., \(R^{2}\), RMSE) for the test sets among different clusters/groups or the total dataset were found to be sensitive to the size of the individual dataset (Table S1). As shown in Table S1, the DL-model is not suitable for small datasets since the \(R^{2}\) score is only \(\sim\)0.60. This suggests that a sample size that is too small in terms of training data will result in poor performance. Compared to the individual small clusters, the \(R^{2}\) score of the entire dataset is significantly better (i.e., \(R^{2}\)\(\sim\)0.90) and might be attributed to the larger size in the training dataset (i.e., with sample size, \(N=1253\)), which contains a wide varieties of ILs system. Interestingly, the similarity in the distribution of \(T_{m}\) among cluster 1 and the entire dataset (Figure 4) guarantees a similar good performance in the high \(R^{2}\) score among these datasets (i.e., \(R^{2}\)\(\sim\)0.90-0.94), despite a smaller sample size, i.e., \(N=605\) (Table S1). To highlight the good predictive capability of our DL model to the entire dataset (\(N=1253\)) in terms of high \(R^{2}\) (i.e., \(R^{2}\)\(\sim\)0.90 in Table 1), Figure S1 depicts the small deviation between the predicted values of melting points and experimentally measured values obtained from the literature. Compared to recent works in the literatures [42; 43; 44; 45; 46], the test \(R^{2}\) score and RMSE reported in this work are outstanding. The previous works in the literature have reported comparable (\(\sim\)25-33 K) or higher (\(\sim\)39-45 K) RMSE values for the melting point prediction (Table 1). Despite being based on different methodologies and datasets, the \(R^{2}\) score reported in the literature [42; 43; 44; 45; 46] (\(\sim\)0.54-0.82) are relatively low or less accurate compared to this work (i.e., \(R^{2}\)\(\sim\)0.90), as shown in Table 1. One of the best performing models in the literatures is based on the kernel ridge regression (KRR) model [46] which uses a significantly lower number of features yet achieves comparable accuracy (i.e., \(R^{2}\)\(\sim\)0.76, RMSE-39 K) to the rest of the studies. As reported by [PERSON] et al. [46], the KRR method only  
Figure 4: The distribution of melting points based on the (**a**) total 1253 ILs dataset, (**b–f**) cluster/group 1-5 ILs dataset that found from k-means clustering analysis. The orange dotted line highlights a boundary with \(T=273\) K that distinguish the low melting (\(T_{m}<273\) K) and high melting point (\(T_{m}>273\) K) ILs system. The median \(T_{m}\) from distribution of (**a–f**) is 279 K, 228 K, 322 K, 333 K, 317 K, 328 K.  
depends on four molecular features or descriptors (e.g., Coulomb matrix, molecular orbital energies) which can, unfortunately, using the ab initio or first-principles calculation data, be computationally costly if a much larger IL dataset and larger IL molecules are considered. For the QSPR model [44], the low \(R^{2}\) (i.e., \(R^{2}\)-0.72) might possibly be attributed to the commonly known sign change problem of descriptors in QSPR when the contributions of a set of selected descriptors or features are analyzed using a multivariate regression model [47]. For the model based on the group contribution (GC) method reported by [PERSON] et al. [42], the RMSE is the smallest, i.e., \(\sim\)25 K, with a high \(R^{2}\) score-0.82 compared to the rest (Table 1). For this method, the contributions of cation or anion functional groups are used to predict the targeted physicochemical property (e.g., \(T_{m}\)).