Prediction of water entry loads and motion trajectories for a delta wing cross medium vehicle using a physics guided LSTM model

During the water entry of cross-medium vehicles, strong transient impacts, complex fluid–structure interaction (FSI), and nonstationary motion trajectories pose challenging problems in computational fluid dynamics (CFD). This study proposes a hybrid temporal surrogate model based on long short-term memory (LSTM) networks and physics-informed neural networks (PINNs) for high-accuracy prediction of water-entry loads and motion trajectories. The dynamic-response data of a delta-wing model under different water-entry velocities and angles are obtained from STAR-CCM+ simulations. The proposed LSTM–PINN framework combines an LSTM network with rigid-body motion equations used as physical-residual constraints to simultaneously predict forces, moments, and displacement trajectories from the STAR-CCM+ data. Compared with the standalone LSTM and PINN baseline models, the proposed LSTM–PINN model achieves lower overall load-prediction errors and better agreement with the CFD load time histories. The integrated displacement trajectories are also in good agreement with the CFD results. Leave-one-condition-out validation at the complete-sequence level indicates that the proposed model has in-domain cross-condition predictive capability for held-out angle–velocity combinations. This model provides a computationally efficient surrogate tool for predicting the water-entry loads and trajectories of cross-medium vehicles while maintaining consistency between the predicted resultant loads and the discrete rigid-body state evolution, thereby providing support for subsequent attitude optimization and real-time control.