## 1 Introduction
It was noticed that the models describe well the systems at low and moderate pressures [33], however, the equations of state suffer from many weaknesses. The equation of state can be reliable only for an individual system and not for more interestingly, multiple systems. They require various adjustable parameters, which should be optimized based on real data within a particular and limited range of thermodynamic conditions. Consequently, developing more general and powerful models to predict the solubility of acid gases, especially carbon dioxide, in ILs is of paramount importance. Recently, many soft computing methods have been applied to model gas solubility and phase equilibrium. One of these methods is the artificial neural network (ANN), which represents an important embranchment computational intelligence method that can be used without any pre-assumption of the input-output relationship [34; 35]. Multilayer perceptron (MLP), radial basis function network (RBF), multi-layer feed-forward network, and gene expression programming (GEP) are the general categories of ANN. Fuzzy logic (FL) is also one of the computational intelligence methods, which can model complicated nonlinear relations [36]. Likewise, the support vector machine (SVM) proposed by [PERSON] was shown to be a very performant smart model [37]. Several researchers have used these smart models in the petroleum industry and to predict the solubility of acid gases in ILs. [PERSON] et al. [36] have predicted CO\({}_{2}\) solubility in the presence of various ILs using MLP and Adaptive Neuro-Fuzzy Inference System (ANFIS). [PERSON] et al. [38] have used MLP, RBF, and ANFIS to predict H\({}_{2}\)S solubility in the presence of various ILs. Otherwise, in 2017, [PERSON] et al. [39] have applied the GEP method to model CO\({}_{2}\) solubility in crude oil during carbon dioxide enhanced oil recovery. The current work aims at developing highly robust and easy-to-use machine learning models that can be applied for forecasting the solubility of CO\({}_{2}\) in 13 different ionic liquids at different temperature and pressure conditions. Two rigorous connectionist techniques, namely multilayer perceptron (MLP), and gene expression programming (GEP) are applied on a set of experimental data that was gathered from different literature sources [40; 41; 42; 43; 44]. The MLP method was optimized using either Levenberg-Marquardt (LMA) or Bayesian Regularization (BR) techniques. The results obtained using three methods (MLP-LMA, MLP-BR, GEP) are then compared with results calculated using thermodynamic models based on Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equation of states. Statistical indicators, including the determination coefficient (R\({}^{2}\)) and Root Mean Square Error (RMSE), are used to evaluate the accuracy of the methods, in addition to graphical assessments using cross plots and bar plots. In the end, outliers detection is performed to test and analyze the validity of the best-developed model and quantify the doubtful experimental points from the database. It is worth noting that the two backpropagation-based learning algorithms (LMA and BR) that were employed in the training process of MLP, alongside the explicit correlations established to predict the CO\({}_{2}\) solubility in ILs, make the current work different from previously published works in the literature. This paper is constructed as follows; Section 2 depicts the data used in the study and the input and output parameters in the models. Section 3 describes in detail the rigorous connectionist models and optimization techniques. An overview of the PR and SRK equations of state is presented in Section 4. In Section 5, the results are presented and discussed, and in Section 6, the conclusions of the study are summarized.