Oil leakage between the slipper and swash plate of an axial piston pump has a significant effect on the efficiency of the pump. Therefore, it is extremely important that any leakage can be predicted. This study investigates the leakage, oil film thickness, and pocket pressure values of a slipper with circular dimples under different working conditions. The results reveal that flat slippers suffer less leakage than those with textured surfaces. Also, a deep learning-based framework is proposed for modeling the slipper behavior. This framework is a long short-term memory-based deep neural network, which has been extremely successful in predicting time series. The model is compared with four conventional machine learning methods. In addition, statistical analyses and comparisons confirm the superiority of the proposed model.