Novel approach for estimating solubility of solid drugs in supercritical carbon dioxide and critical properties using direct and inverse artificial neural network (ANN)

In this work, a hybrid method based on neural network and particle swarm optimization (PSO) was applied to literature data to develop and validate a model that can predict with precision the solubility of binary systems (CO₂ + solid drugs). ANN was used for modeling the nonlinear process. The PSO was used for two purposes: replacing the standard backpropagation in training the ANN and optimizing the process. The training and validation strategy has been focused on the use of a validation agreement vector, determined from linear regression analysis of the predicted versus experimental outputs, as an indication of the predictive ability of the neural network model. Statistical analysis of the predictability of the optimized neural network model trained with trainpso algorithm shows excellent agreement with experimental data. Furthermore, the comparison in terms of average relative deviation (AARD%) between the predicted results for each binary for the whole temperature and pressure range and results predicted by density-based models and a set of equations of state shows that the ANN–PSO model with optimized configuration, five neurons in input and hidden layers and one neuron in output layer (5-5-1) correlates far better the solubility of the solid drugs in scCO₂. A control strategy was also developed by using the inverse artificial neural network method. The sensitivity analysis showed that all studied inputs have strong effect on the solubility and allowed the estimation of some solid properties from the solubility data with good accuracy without need to the group contribution methods.