Robust modelling of solubility in supercritical carbon dioxide using Bayesian methods

Two sparse Bayesian methods were used to derive predictive models of solubility of organic dyes and polycyclic aromatic compounds in supercritical carbon dioxide (scCO₂), over a wide range of temperatures (285.9-423.2 K) and pressures (60-1400 bar): a multiple linear regression employing an expectation maximization algorithm and a sparse prior (MLREM) method and a non-linear Bayesian Regularized Artificial Neural Network with a Laplacian Prior (BRANNLP). A randomly selected test set was used to estimate the predictive ability of the models. The MLREM method resulted in a model of similar predictivity to the less sparse MLR method, while the non-linear BRANNLP method created models of substantially better predictivity than either the MLREM or MLR based models. The BRANNLP method simultaneously generated context-relevant subsets of descriptors and a robust, non-linear quantitative structure-property relationship (QSPR) model for the compound solubility in scCO₂. The differences between linear and non-linear descriptor selection methods are discussed.