Flow field prediction with self-supervised learning and graph transformer: A high performance solution for limited data and complex flow scenarios

To address the challenges of limited labeled data and insufficient global feature extraction in flow field prediction, this paper proposes a modeling approach that combines self-supervised learning and Graph Transformer. The self-supervised learning module leverages feature reconstruction tasks and contrastive learning tasks to fully exploit the latent information in unlabeled data, thereby enhancing the joint modeling capability for local and global features. The Graph Transformer incorporates a self-attention mechanism, enabling effective modeling of long-range dependencies and multiscale features in complex flow fields. Experimental results demonstrate that, under 100% labeled data conditions, the proposed method reduces the root mean squared error achieved by graph convolutional network and a multiscale graph neural network model on the cylinder flow and airfoil flow datasets from 0.970 and 0.561 to 0.616 and 0.305, achieving significant accuracy improvements of 36.5% and 45.6%, respectively. Under 50% labeled data conditions, the method still exhibits outstanding robustness, with RMSEs of 0.792 and 0.390, respectively. The ablation studies reveal that the feature reconstruction and contrastive learning tasks exhibit strong complementarity, achieving optimal performance when jointly employed. Furthermore, the self-attention mechanism significantly enhances the modeling of global features, demonstrating its effectiveness in capturing complex dependencies. The proposed method demonstrates superior prediction accuracy and robustness under limited labeled data and complex flow field conditions, providing an efficient solution for flow field modeling with broad application potential.