A physics-informed deep learning model to reconstruct turbulent wake from random sparse data

This study develops a flexible deep learning framework aimed at reconstructing the global turbulent wakes from the randomly distributed sparse data. The framework is based on a Generative Adversarial Networks where the generator utilizes U-Net architecture and a constraint module is integrated into the training process. It is designed to overcome challenges posed by the chaotic behavior of turbulent fields, randomness in sensor layouts, and sparse sensor numbers. The efficacy of the model is validated across three high-fidelity datasets, including laminar wake behind a circular cylinder, turbulent wake behind a circular cylinder, and turbulent wake behind a square cylinder. The proposed model demonstrates the ability to accurately reconstruct flow patterns of both turbulent and laminar wakes, even utilizing merely 0.043% of the data from the target flow field. The proposed model exhibits significant generalization capability, which means that the model has a nearly independence from the distributions of sensors and a robust adaptation across the inputs with unseen sensor numbers. Ablation studies elucidate the distinct and complementary roles of each module within the model. Additionally, the behavior of the bottleneck tensor is analyzed through visualization, including comparisons with the lift coefficient, quantitative analyses and dimensionality reduction. These visualizations confirm the ability of the model to extract distinctive phase information reliably from sparse data, thereby guiding the reconstruction of global flow patterns. These findings highlight the potential of the model for applications in fluid dynamics where data is collected in a variable manner.