Combination of machine learning and COSMO-RS thermodynamic model in predicting solubility parameters of coformers in production of cocrystals for enhanced drug solubility

Abstract

In this study, we develop predictive models for three target variables, denoted as ${\delta }_d$, ${\delta }_p$, and ${\delta }_h$ using a dataset with 86 features and 181 samples. The response parameters, which are Hansen solubility parameters, were correlated to input parameters via several machine learning techniques. The input features are molecular descriptors of coformers which are calculated based on COMSO-RS thermodynamic model and group contribution approach. The analysis includes outlier detection via Cook's distance, normalization with a min-max scaler, and feature selection through L1-based methods. Three regression models—Gaussian Process Regression (GPR), Passive Aggressive Regression (PAR), and Polynomial Regression (PR)—are employed, with hyperparameter optimization achieved using Transient Search Optimization (TSO). The results indicate that for ${\delta }_d$, the PAR model outperforms others with an R² score of 0.885, RMSE of 0.607, MAE of 0.524, and a maximum error of 1.294. The GPR model shows slightly lower performance with an R² of 0.872, RMSE of 0.816, MAE of 0.579, and a maximum error of 2.755 for ${\delta }_d$. The PR model performs on ${\delta }_d$ with an R² of 0.814, RMSE of 0.923, MAE of 0.597, and a maximum error of 2.814. For ${\delta }_p$, the GPR model provides the best performance, achieving an R² score of 0.821, RMSE of 1.693, MAE of 1.391, and a maximum error of 3.457. The PAR model performs on ${\delta }_p$ with an R² of 0.740, RMSE of 2.025, MAE of 1.980, and a maximum error of 6.609. Also, The PR model predicts ${\delta }_p$ with a R² of 0.7, RMSE of 2.329, MAE of 2.02, and maximum error of 6.366. Similarly, for ${\delta }_h$, the GPR model again shows superior performance with an R² score of 0.983, RMSE of 1.243, MAE of 1.005, and a maximum error of 2.577. The PAR model also accurately predicts ${\delta }_h$ with a R² of 0.924, RMSE of 2.713, MAE of 2.416, and maximum error of 6.307. Additionally, the PR model predicts ${\delta }_h$ with a R² of 0.927, RMSE of 2.757, MAE of 2.334, and maximum error of 8.064. These results highlight the efficacy of the chosen models and optimization techniques in accurately predicting the specified outputs, demonstrating significant potential for application in relevant predictive modeling tasks.