Spatio-temporal graph neural network for multi-step prediction of cylinder water entry flow fields

This study introduces a Spatio-Temporal Graph Neural Network (ST-GNN) for the multi-step prediction of highly dynamic cylinder water entry flow fields. The proposed model integrates a Graph Neural Network (GNN) to capture complex spatial dependencies on unstructured meshes with a Long Short-Term Memory (LSTM) network to model temporal evolution. We generate a dataset from numerical simulations across different cases, varying both Froude numbers and initial entry angles. Extensive ablation studies are conducted to systematically optimize the model's architecture and hyperparameters, revealing that a single-step prediction strategy with an input sequence of eight timesteps yields the most robust performance, significantly reducing error accumulation in long-term prediction. The optimized model achieves high accuracy (R2>0.97) and successfully predicts key physical phenomena during water entry. Furthermore, generalization tests on unseen cases demonstrate the model's excellent interpolation capability within the training data range and reveal the challenges of extrapolation, particularly for the complex phase interface. Crucially, while the multi-step prediction of the velocity field degrades due to error accumulation, the inferred prediction of the water volume fraction remains remarkably stable. This indicates that the model has learned not just the instantaneous spatial correlations between the fields, but more importantly, has captured the underlying temporal dynamics that govern the evolution of the phase interface.