Abstract: Hydraulic support displacement not only determines the cutting trajectory of the coal mining machine and the shape of the body of the scraper conveyor, but also directly reflects the straightness of the entire working face, and the perception and prediction of displacement is extremely important to the intelligent development of the comprehensive mining working face. Currently, displacement sensing mainly relies on hardware means such as displacement and angle sensors and inertial measurement units to obtain hydraulic support movement information. However, under the influence of the complex underground environment, these sensors often have problems such as low measurement accuracy, weak anti-interference ability, and easy accumulation of data errors, which make it difficult to fully meet the accuracy and reliability requirements of the field in practical applications. In addition, the existing methods focus on the motion changes of single rod or point, ignoring the dynamic coupling between the push rod and the center groove in space and time, which leads to the deviation of the overall prediction results. To address the above problems, this paper proposes a nudge displacement prediction method that combines Graph Neural Network (GNN) with Long Short-Term Memory (LSTM) for physical information, and investigates the semantic segmentation based on Segment Anything Model (SAM). A center of mass feature extraction method based on Segment Anything Model (SAM) semantic segmentation is investigated to achieve center of mass detection without large-scale manual annotation; the spatial coupling relationship between the nudging rod and the central groove is modeled by GNN, and an end-to-end prediction framework is constructed by utilizing Long Short-Term Memory Network to capture the temporal features and introducing physical information based on the center of mass velocity. The experimental results show that the prediction performance of the proposed method is significantly better than that of the traditional LSTM, with a reduction of about 73%, 57%, and 34% in the metrics of mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE), respectively. The method provides a new research idea and innovative approach for hydraulic bracket pushover displacement prediction and multi-rigid body dynamic system modeling.