To address the issue of high energy consumption in electro-hydraulically driven rock drills, a hybrid energy consumption prediction model integrating physics-informed and data-driven approaches is proposed. First, a physical model of energy transfer is established based on the working principle of the hydraulic rock drill. Rock drilling experiments reveal the influence of the pressure parameter matching mechanism on energy consumption. Excessively high impact pressure significantly increases both the rate of penetration (ROP) and energy consumption, insufficient propulsion pressure tends to cause idle drilling thereby increasing energy consumption, and excessively high buffer pressure reduces impact efficiency and increases energy consumption. Meanwhile, rock properties significantly affect pressure regulation strategies. Soft sandstone exhibits an optimal pressure range, medium-hard limestone achieves the best energy efficiency in the low-pressure range, and hard granite requires high pressure to activate efficient fragmentation. Finally, with the physical model serving as the core framework, a hybrid data-driven compensation model is constructed using Least Squares Support Vector Machine (LSSVM) optimized by the sine cosine algorithm (SCA). Experimental results show that the hybrid model achieves a coefficient of determination (R2) of 0.99, a mean absolute percentage error (MAPE) of 2.18%, and a root mean square error (RMSE) of 59.45 kJ, outperforming both pure data-driven models LSSVM, Random Forest (RF), Multi-Layer Perceptron (MLP), and Gaussian Process Regression (GPR), as well as the pure physical model. By ensuring interpretability through the physical framework and dynamically correcting unmodeled errors with a data-driven compensation mechanism, the model achieves synergistic improvement in accuracy and reliability.