*2.3. Artificial Neural Network Modelling*

The applicability of the artificial neural network models for predicting the DES pH values based on the σ profiles was also studied. The best neural network was chosen based on the following criteria: *R*<sup>2</sup> and *RMSE* for training, test, and validation sets taking into account the number of neurons in the hidden layer. The properties of the created networks that were chosen are shown in Table 3. Based on the goodness of fit and validation error and considering the number of neurons in the hidden layer, the MLP model 10-5-1 was selected as optimal. Fewer neurons in the hidden layer make the ANN architecture simpler. The selected ANN was characterized by 10 neurons in the input layer, 5 neurons in the hidden layer, and 1 neuron in the output layer. The hidden activation function for the selected ANN was Tanh while the output activation function was Logistic. The described ANN provides a good agreement between the experimental data and the data predicted by the model (*R*<sup>2</sup> validation = 0.9797, *RMSE*validation = 0.0012). As presented in Figure 1c, it can be observed that the data are distributed around the fitted function and that there are no evident outliers. As for the MLP and PLR models, the residual analysis was also performed for the ANN model (Figure 2c) and confirmed the ANN model's goodness of fit through a normal probability plot of the residuals (Figure 2c), residuals versus the predicted values plot (Figure 2c), histogram of the residuals (Figure 2c), and residuals versus the order of the data plot (Figure 2c).

**Table 3.** Architecture of the developed ANN (selected network is marked in bold). The numbers in the network name denote the number of neurons in the input, hidden, and output layers, respectively.


Based on the presented results, it can be concluded that the σ profiles are good molecular descriptors of DESs since the mathematical correlation of the experimental and predicted values is high. Moreover, based on the obtained *R*<sup>2</sup> values and the residual analysis, it can be concluded that both the PLR and ANN model can be efficiently applied for the prediction of the DES pH values based on the σ profiles. Due to the simplicity of the PLR model, this model is proposed for the prediction of physicochemical properties.

#### *2.4. MLR, PLR, and ANN Models' Independent Validation*

Validation of the MLR, PLR, and ANN models developed for the prediction of the DES pH values based on the σ profiles was performed on the independent set of data. The validation set included the σ profiles of 16 DESs. Comparisons between the experimental data and model-predicted data are shown in Figure 2. The validation performance of the developed models was estimated based on *R*<sup>2</sup> and *RMSE* and the obtained values were as follows: (i) for MLR *R*<sup>2</sup> = 0.7097, *RMSE* = 1.1140; (ii) for PLR *R*<sup>2</sup> = 0.8605, *RMSE* = 0.7652; and (iii) for ANN *R*<sup>2</sup> = 0.8885, *RMSE* = 0.82926.

It can be noticed that all three proposed models predict the pH value with high accuracy. As expected, the highest *R*<sup>2</sup> between the experiment and model-predicted data was obtained for ANN prediction of the analyzed DES pH values while the lowest *R*<sup>2</sup> between the experiment and model-predicted data was obtained for the MLR model. These findings demonstrate that σ profile ANN modeling is a useful and reliable method for predicting DES pH values based on the σ profiles. Nevertheless, considering RMSE, it can be noticed that the PLR model can efficiently be used for the prediction of pH values based on the σ profiles. As described, the *R*<sup>2</sup> values are scaled between 0 and 1, whereas the RMSE is not scaled to a specific value and, therefore, provides explicit information about how much the prediction deviates.

As stated before, it was relatively easy to link the parameters of the MLR and PLR models to their physical significance. On the other hand, ANNs, by definition, belong to a class of agnostic models and, thus, it is difficult, if not impossible, to reveal their physical meaning. At the same time, this is the reason why they behave much better in interpolation than in extrapolation. The independent validation presented here may be considered as interpolation since the DES members of the independent validation dataset belong to the same DES classes as those used for constructing the model. However, given the rather simple and rather clear relation between the σ profile and pH as revealed by MLR, there is no true reason to believe that the models would behave poorly in extrapolation, even for ANN, i.e., for DES classes not involved in the development of the models. However, this is yet to be checked, e.g., for DESs based on metal chlorides or DESs containing ionic liquids, etc.

The current literature data refer to the prediction of other physicochemical properties (such as viscosity and density) and only a narrow range of values characteristic for limited groups of structurally related DESs [11–14]. Based on our current knowledge, only one study has investigated the development of a mathematical model for DES pH value prediction [13]. In that study, the pH literature data of 41 DESs were processed in a similar way using the COSMO-RS and mathematical models, MLR and ANN, also covering a variety of cations, anions, and functional groups. The literature study [12] used literature data and included different temperatures (with temperature as an input parameter) while our study used our data obtained at a single temperature. The literature study also showed the potential of MLR and ANN modeling for the prediction of the pH value, however, with more complex models (models with more coefficients) than those developed in this work. Taking into consideration the specific future application of the developed models, it is recommended that they are as simple as possible and as robust as possible. Summing up the presented results, it can be concluded that the PLR model developed in this research can efficiently be used for the prediction of a wide range of DES pH values based on the σ profiles.

#### **3. Materials and Methods**

#### *3.1. Materials*

Betaine, choline chloride, glucose, L-(−)-proline, oxalic acid, sucrose, sorbitol, and xylitol were all purchased from Acros Organics, USA. Citric acid, D-fructose, D-(+)-xylose, D,L-malic acid, ethylene glycol, glycerol, and urea were all purchased from Sigma-Aldrich, USA. BIOVIA TmoleX19 version 2021 software (Dassault Systèmes, Vélizy-Villacoublay, France) was used for geometry and energy optimization of the HBAs and HBDs used in this study. BIOVIA COSMOtherm 2020 version 20.0.0. software (Dassault Systèmes) was used for the σ profile calculations of the defined DESs.

#### *3.2. Methods*

#### 3.2.1. DES Preparation

DESs were prepared by mixing defined molar ratios of HBA to HBD. The two or more components were weighed in a specific ratio in a round-bottomed glass flask, adding 10–50% (*w*/*w*) of water. Then, the flasks were sealed, and the mixtures stirred and heated to 50 ◦C for 2 h until homogeneous transparent colorless liquids formed. The DES abbreviations and corresponding molar ratios are given in Table 1.
