Separation process modeling and analysis in water purification based on membrane technology using artificial intelligence models

This study investigates the application of four machine learning models to evaluate the membrane separation process. The used models included Multiple Linear Regression (MLR), Gradient Boosting Decision Trees (GBDT), Kernel Ridge Regression (KRR), and Neural Oblivious Decision Ensembles (NODE). The models were used to predict concentration levels based on spatial coordinates as inputs. The models were optimized using Differential Evolution (DE) to enhance the mean R 2 score through tenfold cross-validation. Performance evaluation relied on parameters: R 2 , Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The NODE model excelled with a test R 2 of 0.9992, demonstrating exceptional accuracy and generalization in analysis of generated dataset. GBDT performed strongly with a test R 2 of 0.9978. In contrast, KRR yielded a test R 2 of 0.9631, while MLR underperformed with a test R 2 = 0.8423. SHAP analysis highlighted z(m) as the primary predictor, with r(m) as a secondary contributor. These results establish NODE and GBDT as the best models for concentration prediction, balancing precision, and interpretability.