Thermal analysis and CFD-assisted machine learning prediction of temperature fields in direct-contact membrane distillation using darts game optimization

Abstract

In this study, three regression techniques—multi-layer perceptron (MLP), Gaussian process regression (GPR), and weighted least squares (WLS)—were evaluated to predict the spatial temperature distribution, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:T$$\end{document} (K), obtained from CFD analysis of a direct-contact membrane distillation unit, using the spatial coordinates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:r$$\end{document}(m) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:z$$\end{document}(m) as input variables. Dart game optimization (DGO) was employed for hyperparameter tuning of all machine learning models to enhance their predictive accuracy. The DGO-tuned Gaussian process regression model (DGO-GPR) exhibited remarkable performance for temperature prediction in the unit operation, achieving \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{R}^{2}$$\end{document} train and test scores of 0.99885 and 0.99907, respectively. These results underscore the efficacy of DGO in optimizing hyperparameters for GPR in the context of thermal analysis of membrane distillation systems. Similarly, the DGO-tuned multi-layer perceptron (DGO-MLP) model exhibited commendable performance, achieving \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{R}^{2}$$\end{document} train and test scores of 0.9947 and 0.99502, respectively. As such, the model demonstrated a modest MAPE of 6.80927E−04 and an RMSE of 3.0333E−01. The DGO-MLP model underscores the versatility of the darts game optimizer across different predictive architectures. Conversely, the DGO-tuned weighted least squares model (DGO-WLS) displayed good performance with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{R}^{2}$$\end{document} train and test scores of 0.88153 and 0.88636. However, the model exhibited a higher MAE of 1.02602E+00, accompanied by a MAPE of 3.12572E−03 and an RMSE of 1.2914E+00. The results indicate that while DGO enhances the performance of WLS, there may be inherent challenges in achieving precision comparable to other models in certain scenarios. The reported predictive performance is specific to the spatial and operating domain of the investigated CFD configuration and should not be interpreted as evidence of generalization to different inlet conditions, membrane geometries, or process configurations without additional parametric CFD data and retraining.