Physics-guided residual U-net for super-resolution reconstruction of two-dimensional vorticity fields

Abstract

High-resolution vorticity fields are essential for identifying vortical structures, capturing shear layers, and analyzing flow mechanisms, yet high-fidelity simulations and experimental measurements are often costly. To recover fine-scale structures from low-resolution flow fields, we propose a physics-guided residual U-Net for 8× super-resolution reconstruction of two-dimensional vorticity fields. The method takes as input a low-fidelity vorticity field obtained by 8× downsampling, followed by bicubic interpolation. An encoder-decoder architecture extracts multiscale flow features, while a global residual connection enables the network to learn the missing high-frequency vortical details. To improve first-order spatial-structure consistency, we introduce a Sobel gradient loss in addition to the MSE loss, constraining the gradient discrepancy between the predicted and reference fields in the x- and y-directions. Experiments are conducted on 999 consecutive snapshots of two-dimensional vorticity fields using a strict temporal split. On 100 unseen test samples, the proposed method achieves an average MSE of 5.4723×10−4 and an average PSNR of 32.66 dB. Compared with bicubic interpolation, it reduces MSE by 35.68% and Sobel gradient error by 15.98%. These results demonstrate that the proposed method effectively recovers dominant vortical structures and high-gradient edge features.