Abstract: Deep learning has garnered significant attention in aircraft design,particularly with the advancements driven by AI for Science.Data-driven methods based on neural networks have achieved remarkable success in airfoil flow field prediction.How-ever,these methods often underperform when labeled data is limited.This paper proposes a semi-supervised learning(SSL) me-thod named Semi-Flow for airfoil flow field prediction.Semi-Flow leverages the memory properties of neural network loss to classi-fy pseudo-labeled data into easy and hard subsets based on loss function values.This clustering method is based on Gaussian mixture model(GMM).The loss function combines data loss with auxiliary physical supervision,ensuring the model's outputs conform to aerodynamic properties and data constraints.During the data selection process,the easy samples common to both mo-dels are chosen as training samples,thereby avoiding the impact of noisy samples.The training process starts with several rounds of warm-up training on the labeled samples,followed by the gradual inclusion of filtered easy samples.Experimental results demonstrate that the Semi-Flow method significantly outperforms models trained solely on limited labeled data,with an overall predictionperformance improvement of nearly 30%.Ablation studies and qualitative results further validate the effectiveness of the proposed method.Semi-Flow exemplifies the potential of AI for Science,offering a promising approach to flow field prediction by reducing the dependency on large amounts of labeled data.

Key words: Deep learning, AI for science, Semi-supervised learning, Flow field prediction