Temporal super-resolution of cavitating hydrofoil velocity fields via few-shot learning with low-cost phase information

In fluid experiments, the temporal resolution of velocity fields is typically constrained by the complexity and high cost of measurement systems. Although recent studies have explored the temporal super-resolution of velocity fields using data-driven approaches, they typically rely on large amounts of high-frequency experimental data for supervised training, resulting in high costs and limited generalization capabilities. To overcome this bottleneck, we focus on cavitating hydrofoil flows and propose a semisupervised deep learning framework, DAIT-DNN (Domain-Adaptive Iterative Transfer Deep Neural Network), which completely eliminates the reliance on external high-frequency velocity datasets. The proposed method innovatively employs low-cost, nonintrusive high-speed imaging to capture high-frequency binary phase fields, which serve as inputs to enable temporal super-resolution reconstruction based on its own sparsely sampled, low-frequency velocity field data. The results demonstrate that, under sparse sampling conditions, DAIT-DNN—integrating pseudolabel assistance, domain adaptation, and an iterative optimization strategy—significantly improves the generalization capability of few-shot modeling compared to conventional DNN models. Particularly, for certain highly unsteady conditions or specific moments, DAIT-DNN trained on low-frequency data even outperforms traditional models trained on high-frequency datasets. By integrating low-cost phase information with few-shot velocity data, this work offers an efficient, economical solution for reconstructing complex cavitating flow fields and broadens the potential applications of deep learning to modeling complex physical systems.