The application of the polynomial regression machine learning method for forecasting the specific heat, density, thermal conductivity, and dynamic viscosity of NiFe2O4-water nano-coolant

Abstract This study proposes a robust hybrid framework integrating Machine Learning (ML), Multi-Objective Optimization (MOO), and Multi-Criteria Decision-Making (MCDM) to accurately predict and optimize the thermophysical properties of a NiFe₂O₄-water nanofluid. A Multiple Polynomial Regression (MPR) model was developed to characterize dynamic viscosity (DV), thermal conductivity (TC), specific heat capacity (SHC), and density (D) as functions of temperature (T) and nanoparticle volume fraction (φ). The model’s predictive accuracy is rigorously validated using eight statistical metrics: correlation coefficient (R), root mean square error (RMSE), mean square error (MSE), Nash–Sutcliffe efficiency (NSE), mean absolute error (MAE), mean absolute percentage error (MAPE), coefficient of determination (R²), and mean absolute relative error (MARE). In the optimization phase, the NSGA-II algorithm was employed to achieve a Pareto-optimal trade-off by maximizing TC and SHC while simultaneously minimizing DV and D. The optimal Pareto front was evaluated using the Shannon entropy method based on four key performance indicators: Maximum Spread (MS), Spacing (SP), computational time, and Mean Ideal Distance (MID). Subsequently, the TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) and MEW (Multiplicative Exponential Weighting) methods were implemented to identify the most suitable optimal configurations. Results demonstrate promising predictive performance of the MPR model within the investigated range, with margin of deviation (MoD) values of − 1.6%, 0.403%, − 0.0206%, and − 0.0516% for DV, TC, SHC, and D, respectively. TOPSIS identified the optimal operating point at φ = 0.3484% and T = 78.63 °C, yielding DV = 0.0004025 kg/m·s, TC = 0.9311 W/m·K, D = 987.0308 kg/m³, and SHC = 4.1668 kJ/kg·K. However, the MEW method proposed an alternative optimal point at φ = 0.1082% and T = 78.19 °C, with corresponding properties DV = 0.000369 kg/m·s, TC = 0.8467 W/m·K, D = 975.889 kg/m³, and SHC = 4.175 kJ/kg·K. This proposed framework provides a practical and interpretable approach to the energy-efficient design of nanofluids, with potential applications in electronic cooling, automotive thermal management, and energy storage systems, pending further validation on independent datasets.