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

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Title: Leveraging machine learning with Bayesian optimization for optimizing feed spacer geometry using insights from predicting Sherwood and Power numbers.
Authors: Sutariya, Bhaumik1,2 (AUTHOR) bhaumiks@csmcri.res.in, Mer, Priyanshi1 (AUTHOR)
Source: Chemical Engineering Communications. 2026, Vol. 213 Issue 4, p647-665. 19p.
Subjects: Machine learning, Dimensionless numbers, Membrane separation, Random forest algorithms, Surrogate-based optimization, Mass transfer coefficients
Abstract: 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 (Sh) and Power number (Pn) 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 (R2), mean absolute error (MAE), and mean square error (MSE). Results indicated CatBoost as the best-performing model, exhibiting R2 values of 0.9985 ± 0.0001 and 0.9958 ± 0.0017 for training and testing phases for Sh, whereas 0.9998 ± 0.0001 for training and 0.9945 ± 0.0029 for testing for Pn. Feature importance analysis highlighted the crucial influence of Re and l / h on output metrics. Bayesian optimization was used to maximize Sh while simultaneously minimizing Pn. 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 (Re ≈ 30), are optimum conditions. The results of the model prediction were compared with the published data. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract: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 (Sh) and Power number (Pn) 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 (R2), mean absolute error (MAE), and mean square error (MSE). Results indicated CatBoost as the best-performing model, exhibiting R2 values of 0.9985 ± 0.0001 and 0.9958 ± 0.0017 for training and testing phases for Sh, whereas 0.9998 ± 0.0001 for training and 0.9945 ± 0.0029 for testing for Pn. Feature importance analysis highlighted the crucial influence of Re and l / h on output metrics. Bayesian optimization was used to maximize Sh while simultaneously minimizing Pn. 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 (Re ≈ 30), are optimum conditions. The results of the model prediction were compared with the published data. [ABSTRACT FROM AUTHOR]
ISSN:00986445
DOI:10.1080/00986445.2025.2572731