A masked autoencoder-based three-dimensional foundation model for vortex identification

Vortex identification is crucial for exploring physical mechanisms in fluid dynamics. Physics-based methods are computationally efficient but lack accuracy in identifying complex vortex structures. Data-driven approaches enable faster and more objective identification but are typically limited to two-dimensional simulations with large amounts of training data and often struggle with generalization. To address these challenges, we propose a Masked Autoencoder-based Three-Dimensional Foundation Model. First, to overcome the difficulty of extending existing pretraining strategies to three-dimensional simulations, we design a pretraining strategy based on a Masked Autoencoder that incorporates a Shifted Window Transformer architecture. By leveraging the sliding window attention mechanism, we reduce computational costs and enhance the model's ability to extract local features in the flow field. Then, to address the issue of sparse training data in real-world simulation scenarios, we fine-tune the pretrained model for vortex identification. Using the encoder's strong feature extraction capabilities from the pretrained model, we perform supervised training to learn the nonlinear mapping between flow field data and ground truth, even under limited data conditions. Finally, to enhance the model's generalization ability, we apply a high masking ratio to reconstruct the partial differential equations (PDEs) data, forcing the model to learn general latent representations. This improves adaptability across diverse physical fields for vortex identification tasks. Extensive experiments conducted on 13 PDE datasets demonstrate the method's effectiveness, showing superior performance in identifying vortex structures in out-of-distribution cases with sparse data.