An accurate viscosity prediction model is essential for the intelligent design and industrial scaling of ionic liquid (IL)-based technologies. This study presents a novel hybrid residual modeling strategy that leverages machine learning to identify and capture systematic deviations in physical modeling. The model was developed using experimental viscosity data for 159 ILs and seven quantum chemical descriptors determined from first-principle. A physics-based viscosity model (COSMO-RS) provides prior knowledge as one example, where systematic deviations follow a power law distribution (n_cosmo = An_exp^B) identified in this work. The proposed model with systematic deviations demonstrates excellent performance compared to the model with random deviations and also outperforms the conventional hybrid and data-driven models, achieving superior predictive accuracy on the test set (R² = 0.993, MAE = 0.04) and reducing the average absolute relative deviation from 52.42 % to 4.49 %. Feature importance results reveal the key descriptors contributing to the systematic deviations: A = f(Polarity), B = f(Sigma, AdE).