Development of advanced hybrid mechanistic-artificial intelligence computational model for learning of numerical data of flow in porous membranes

Numerical analysis and machine learning regression were carried out for understanding and description of ozonation process combined with membrane separation. The main focus was on mass transfer modeling to simulate concentration distribution of ozone in liquid phase. Machine learning regression models were utilized to decrease the computational expenses of CFD (Computational Fluid Dynamics) simulations. For machine learning models, we compared the performance of three regression models, namely Gaussian Process Regression (GPR), Deep Neural Network (DNN), and Extreme Gradient Boosting (XGB or XGboost) for predicting the obtained output of CFD simulations which was ozone concentration in the feed, i.e., C (mol/m3) as function of radial and axial coordinates. Hyper-parameter tuning for these models was performed using the Tabu Search algorithm. The results indicate that both GPR and DNN models achieved excellent prediction accuracy, with R-squared values of 0.99999 and 0.99998, respectively. Also, the RMSE for GPR and DNN were 3.8481E-03 and 4.9835E-03, respectively, while their maximum errors were 6.08501E-02 and 4.47909E-02, respectively. On the other hand, the XGB model showed a lower performance, with an R-squared value of 0.99402, an RMSE of 8.9484E-02, and a maximum error of 4.51381E-01