Deep learning models to predict CO2 solubility in imidazolium-based ionic liquids

Abstract

This study focuses on predicting CO₂ solubility in imidazolium-based ionic liquids using deep learning models with input parameters of critical pressure, critical temperature, molecular weight, and acentric factor. The models evaluated include Bayesian Neural Networks (BNN), Deep Neural Networks (DNN), Gradient Boosting Neural Networks (GrowNet), Tabular Neural Networks (TabNet), Random Forest (RF), and Support Vector Regression (SVR). The results were compared with two PC-SAFT models, namely cQC-PC-SAFT-MSA (1) and cQC-PC-SAFT-MSA (2), where deep learning models performed better than SAFT models. Graphical and statistical analyses revealed that the GrowNet model, with a root mean square error of 0.0073 and a coefficient of determination of 0.9962, exhibited the lowest error compared to other models. In addition, Pearson correlation coefficient (PCC) and Shapley additive description (SHAP) analyses highlighted pressure (P) as a key parameter determining CO₂ solubility in imidazolium-based ionic liquids, significantly contributing to model performance.

Keywords: CO2 solubility; Deep learning; GrowNet; Imidazolium-based ionic liquids; TabNet.

Fig. 1

Distribution of data points for various ILs included in this study.

Fig. 2

Heat map for the input and target variables in the collected database.

Fig. 3

Mean absolute error (MAE%) values for the four developed deep learning models compared with PC-SAFT and traditional machine learning models.

Fig. 4

Taylor plot illustrating the accuracy of deep learning and PC-SAFT models (ETM-1 and ETM-2) compared to experimental values.

Fig. 5

Cross-plot of the models used in this study to predict CO₂ solubility.

Fig. 6

Error distribution plot of the presented models used to predict CO₂ solubility.

Fig. 7

Cumulative frequency curves of the models: (a) deep learning models alongside ETM-1 and ETM-2; (b) deep learning models only.

Fig. 8

Histograms of residuals (exp-pred) for the developed correlations to predict CO₂ solubility.

Fig. 9

Group error plot for CO₂ solubility prediction by different models.

Fig. 10

Absolute error distribution by input features for all proposed models.

Fig. 11

Absolute error (%) comparison of all models for the ILs studied in this work.

Fig. 12

Box and Whisker diagram showing the residual error of the GrowNet model for different ILs.

Fig. 13

(a) Effect of temperature change on CO₂ solubility in [C₂mim [Tf₂N] at a constant pressure of 2000 kPa, (b) effect of pressure change on CO₂ solubility in [C₂mim [DCA] IL at a constant temperature of 298.2 K, (c) comparison of CO₂ solubility in [C₂mim][Tf₂N] at 295.1 K and 298.15 K.

Fig. 14

The SHAP value distribution for each sample, with input features ranked based on their importance.