Computational hybrid analysis of drug diffusion in three-dimensional domain with the aid of mass transfer and machine learning techniques

Molecular diffusion of drugs is of major importance for development and understanding drug delivery systems. Indeed, the main phenomenon which is controlling the rate of release is molecular diffusion which can be controlled via different phenomena such as interactions with the drug carrier and solution. In this work, we developed a novel hybrid model based on mass transfer and machine learning for predicting drug diffusion in a 3D space. The mass transfer equation including diffusion is solved in the domain and then the data is extracted for building machine learning models. The present study presents the findings of an analysis conducted with the objective of constructing precise regression models for the prediction of chemical species concentration (C) for a drug diffusion through a three-dimensional space, utilizing coordinates (x, y, z). The dataset comprises over 22,000 data points, with each point containing the coordinates ([Formula: see text]) and the corresponding concentration (C) in mol/m³. We employ three tree-based ensemble models: Kernel Ridge Regression (KRR), [Formula: see text]-Support Vector Regression ([Formula: see text]-SVR), and Multi Linear Regression (MLR) for modeling the relationship between spatial coordinates and the concentration. Hyperparameter optimization is performed using the Bacterial Foraging Optimization Algorithm (BFO) to fine-tune the models. The results reveal that [Formula: see text]-SVR has the highest performance with a score of 0.99777 in terms of R², followed by KRR with an R² score of 0.94296, and MLR with an R² value of 0.71692. Additionally, [Formula: see text]-SVR exhibits the lowest RMSE and MAE, showing excellent predictive accuracy compared to KRR and MLR. Overall, our analysis demonstrates the effectiveness of employing tree-based ensemble models coupled with BFO for accurately predicting chemical concentrations in three-dimensional space, with [Formula: see text]-SVR emerging as the most promising model for this task. These findings have implications for various applications such as environmental monitoring, pollutant dispersion modeling, and chemical process optimization.