Microwave dielectric response of methylene blue aqueous solutions: Havriliak–Negami modelling and explainable machine learning

The dielectric and electric properties of aqueous solutions of methylene blue (MB) were investigated in the frequency range of 200 MHz to 20 GHz and in the temperature range of 293.15 K-323.15 K. Solutions with different MB weight fractions (W) were prepared using distiled water (DW), and their (ε∗(f), (σ ac′), and tan δ were measured using an Anritsu MS46322A VNA. The dielectric response deviates from Debye behaviour due to ionic conduction and can be well described by the HN + σ. Experimental measurements were combined with machine‑learning models to predict ε′ and ε” using leakage-free Group K-Fold validation. Of the six algorithms tested—Ridge Regression, Random Forest (RF), Gradient Boosting (GB), XGBoost, Support Vector Regression (SVR) and Multi-Layer Perceptron (MLP)—XGBoost had the most accurate predictions, with R2 values of 0.998985 and 0.990213 for ε′ and ε”, respectively. SHAP analysis showed frequency as the predominant governing factor of the dielectric response.