What question did this study set out to answer?

The study aims to develop a computational method for estimating pharmaceutical solubility in supercritical carbon dioxide under varying conditions using machine learning.

March 28, 2026Open Access

Advanced simulation and numerical evaluation of pharmaceutical solubility estimation under supercritical processing using artificial intelligence computations

AAAhmed H. AlbariqiJazan University RARami M. AlzhraniTaif University MAMajed A. AlghamdiKing Abdulaziz University

Key Points

The study aims to develop a computational method for estimating pharmaceutical solubility in supercritical carbon dioxide under varying conditions using machine learning.
Developed computational models for solubility estimation in SC-CO2
Utilized experimental data combined with machine learning techniques
Implemented convolutional neural networks, multilayer perceptron, and deep neural networks
Applied the Dragonfly Algorithm for hyper-parameter optimization
MLP model achieved an R-squared score of 0.99093 for solubility prediction
CNN and DNN models had R-squared scores of 0.97218 and 0.98625, respectively
MLP model achieved an R-squared score of 0.99911 for predicting SC-CO2 density
DNN and CNN models scored 0.94799 and 0.88958 for solvent density prediction

Abstract

Poor aqueous solubility of medicines has been a subject of great interest for improvement of pharmaceutical industry. Computational analysis of solubility data is of great importance for evaluation of supercritical processing which can be used to enhance drugs solubility. A computational method for estimating the solubility of pharmaceuticals in supercritical carbon dioxide (SC-CO2) at varying processing conditions was developed using machine learning. Leveraging an innovative combination of experimental data and advanced machine learning techniques, this study investigates the prediction of both SC-CO2 solvent density and glibenclamide solubility. The dataset utilized in this study encompasses a range of temperature and pressure values, alongside corresponding solvent densities and solubility outcomes. Employing a diverse array of machine learning models, including convolutional neural network (CNN), multilayer perceptron (MLP), and deep neural network (DNN) architectures, predictive modeling was conducted to elucidate the complex relationships embedded within the dataset. These models were fine-tuned using the innovative Dragonfly Algorithm (DA) for hyper-parameter optimization, further enhancing their predictive capabilities. For solubility prediction, the MLP model achieved an outstanding R-squared score of 0.99093, underscoring its proficiency in capturing intricate solubility patterns. The CNN and DNN models closely followed suit, with R-squared scores of 0.97218 and 0.98625, respectively. Additionally, the study was extended to predict the density of SC-CO₂, a crucial factor in solubility dynamics. Here again, the MLP model outshone the others with a staggering R-squared score of 0.99911. The DNN and CNN models achieved commendable R-squared scores of 0.94799 and 0.88958, underscoring their adeptness in capturing the intricate interplay between temperature, pressure, and solvent density. These results demonstrate that data-driven models can reliably capture the coupled effects of temperature, pressure, and solvent density on drug solubility, providing a practical predictive framework for supercritical pharmaceutical process design.

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