Precise Modeling of Rheological Behavior for a Magnetic Nanofluid Comprising Iron and Copper Oxide Nanoparticles using Various Machine Learning Models

• prediction of the viscosity (μ nf ) of nanofluids consisting of iron (Fe) and copper oxide (CuO) • using an artificial neural network (ANN) model. • In this study, 8 regressions were used to predict and numerically model μ nf . • 3 surface diagrams were created to determine μ nf . • the trained sample can predict well all the observed and unobserved data during the testing process. This study examined the prediction of viscosity (μ nf ) in binary nanofluid mixtures of water and ethylene glycol (EG) containing iron (Fe) and copper oxide (CuO) using machine learning (ML) models. Eight regression techniques were employed in this research: linear regression (Linreg), decision tree regression (D-Treereg), generalized linear regression (genLin), support vector machine (SVM), artificial neural network (ANN), least-squares boosting (LSBoost), bagging regression, and Gaussian process regression (GPR). To assess the performance of each method, 1,000 repetitions were performed for each model. The resulting data were evaluated using five performance metrics: Pearson's Linear Correlation Coefficient (PLCC), Spearman's Rank Order Correlation Coefficient (SROCC), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Maximum Absolute Error (ME). The findings reveal that the GPR method outperformed all other techniques, achieving higher correlation and lower error values. Specifically, the GPR model with the ARD Squared Exponential kernel achieved the best performance, with PLCC, RMSE, and MAE values of 0.9991, 0.1903, and 0.1239, respectively. Additionally, GPR models employing Ard Rational Quadratic and ArdMatern32 kernels produced the highest SROCC (0.9983) and ME (0.5339). The superior predictive capability of the GPR method was further corroborated by additional analyses, including scatter diagrams that compared actual and predicted μ nf values. The efficacy of the GPR approach was further confirmed by a 20-bin error histogram illustrating the discrepancies between actual and predicted values. Ultimately, surface plots generated using shear rate (SR), temperature (Temp), and solid volume fraction (φ) demonstrated the model's capacity to reliably predict both observed and unobserved data throughout the testing process.