Bicubic Fourier neural operator for Super-Resolution Reconstruction of Turbulent Flows

The reconstruction of high-resolution flow fields from low-resolution data remains a persistent challenge within fluid dynamics. Super-resolution using deep learning is a valuable tool for enhancing visualizations of flow fields to recover detailed features from low-resolution data. This work introduces the Bicubic Fourier Neural Operator (Bicubic FNO), which combines the benefits of both bicubic interpolation and FNO. We compare our architecture against standard FNO and two convolutional neural network (CNN) models, namely, Super-Resolution CNN (SRCNN) and downsampled skip-connection/multiscale model (DSC/MS) reported in the literature. We tested our model on two-dimensional decaying homogeneous isotropic turbulence and achieved improved reconstruction accuracy. Quantitatively, the Bicubic FNO model achieves a 10.47% improvement over the standard FNO and a 19.59% improvement over the DSC/MS model in terms of Peak Signal-to-Noise Ratio (PSNR). Moreover, for a similar performance, the Bicubic FNO led to a significant reduction of 74% in parameter count over standard FNO, demonstrating its computational efficiency.