The screw motor generates downhole annular pressure drop through fluid drive during the drilling process, and accurate prediction of this pressure drop is crucial for ensuring drilling safety and stable operation. Traditional physical models, constrained by idealized assumptions, are limited in fully reflecting the multi-source coupling characteristics, while purely data-driven methods are susceptible to data quality and external disturbances, leading to insufficient model generalization.To address these issues, DeepONet (deep operator network) was integrated with physical constraints, and an improved DON-PINN model based on physical information neural networks was proposed. The model directly learns the complex mapping relationship between input and output by incorporating the flow mechanism of the screw motor into the loss function, while using the wellbore annular fluid dynamics equation as a physical constraint to ensure the consistency and accuracy of the prediction results. Based on experimental data obtained from a self-designed screw motor pressure drop system, the performance of the DON-PINN model was compared with that of MLP (multilayer perceptron) and FCNN (fully connected neural network). The results showed that DON-PINN outperformed the two traditional methods in terms of training efficiency, prediction accuracy, and generalization ability, and was able to accurately capture the nonlinear trends of pressure drop with changes in parameters under the dominance of different variables. This approach, by combining physical mechanism constraints with data-driven learning capabilities, provided a new solution for predicting the pressure drop effect of downhole screw motors and had the potential to improve operational safety and continuity under complex drilling conditions.