Leveraging machine learning with Bayesian optimization for optimizing feed spacer geometry using insights from predicting Sherwood and Power numbers

This study utilized machine learning (ML)-based models, including Random Forest (RF), Multilayer Perceptron (MLP), Gradient Boosting Machine (GBM), Extreme Gradient Boosting (XGB), and Categorical Boosting (CatBoost), to predict Sherwood number (<i>Sh</i>) and Power number (<i>Pn</i>) based on geometrical features of the feed spacers (i.e., α,β, and l/h) and crossflow rate (Re) of the membrane-based separation plants. The performance of each model was evaluated using key statistical metrics, including the coefficient of determination (<i>R</i>²), mean absolute error (MAE), and mean square error (MSE). Results indicated CatBoost as the best-performing model, exhibiting <i>R</i>² values of 0.9985 ± 0.0001 and 0.9958 ± 0.0017 for training and testing phases for <i>Sh</i>, whereas 0.9998 ± 0.0001 for training and 0.9945 ± 0.0029 for testing for <i>Pn</i>. Feature importance analysis highlighted the crucial influence of Re and l/h on output metrics. Bayesian optimization was used to maximize <i>Sh</i> while simultaneously minimizing <i>Pn</i>. The results suggest that lower values of α (ranging from 7.5° to 22.1°), mid-range values of β (86.2° to 95.7°), and lower values of l/h (between 3 and 4.1), along with a low cross-flow rate (<i>Re</i> ≈ 30), are optimum conditions. The results of the model prediction were compared with the published data.