PhysSFI-Net: physics-informed geometric learning of skeletal and facial interactions for orthognathic surgical outcome prediction

Orthognathic surgery repositions jaw bones to restore occlusion and enhance facial aesthetics. Accurate simulation of postoperative facial morphology is essential for preoperative planning. This study aims to develop and validate a physics-informed geometric deep learning framework named PhysSFI-Net for precise prediction of soft tissue deformation following orthognathic surgery. The model integrates a hierarchical feature extraction module with attention mechanisms to capture skeletal-facial interactions, an LSTM-based sequential predictor for incremental deformation, and a biomechanics-inspired reconstruction module for high-resolution facial modeling. The model was trained on 135 patients and externally validated on an independent cohort of 33 patients. Model performance was assessed using point cloud shape error, surface deviation error and landmark error between predicted facial shapes with corresponding ground truths. Quantitative analysis demonstrated that PhysSFI-Net achieved a global shape error of 1.070 ± 0.088 mm, a surface deviation error of 1.296 ± 0.349 mm and a landmark error of 2.445 ± 1.326 mm. Comparative experiments indicated that PhysSFI-Net outperformed the state-of-the-art method ACMT-Net and baseline models. External validation further confirmed its robustness with a global shape error of 1.431 ± 0.087 mm and consistently lower subregional and mesh-based errors. In conclusion, PhysSFI-Net enables interpretable, high-resolution prediction of postoperative facial morphology, showing strong potential for clinical application in orthognathic surgical planning.