A physics-informed convolutional network based on feature fusion for high-resolution flow field reconstruction from sparse and noisy data

Reconstructing high-resolution flow fields remains a significant challenge in fluid mechanics due to the limitations of measurement techniques. In recent years, physics-informed neural networks (PINNs) have been proposed to reconstruct flow fields by embedding physical constraints. However, accurate solutions are difficult to obtain when faced with complex fluid properties or high noise levels. Therefore, a physics-informed convolutional network based on feature fusion (FFPICN) is proposed to reconstruct high-resolution flow fields from sparse and noisy velocity data. The framework mainly consists of a feature extraction module and a physical information module. Unlike traditional PINNs that mainly rely on fully connected networks to extract features, the new feature extraction module comprises a parallel convolutional layer, a feature fusion layer, and a convolutional fusion module to extract and fuse shallow and deep fluid features. The spatial feature extraction ability of convolutional neural networks is used to enhance the ability to capture small-scale fluid structures. The physical information module embeds the constraints of the transformed Navier–Stokes equations into deep features to improve the accuracy of flow field reconstruction. Furthermore, a preprocessing technique is designed to linearly transform the data and the Navier–Stokes equations concurrently. Finally, wake and turbulence data are investigated at different levels of sparsity and noise. Experimental results show that FFPICN can reconstruct high-resolution flow fields even at 1% sparsity or 20% noise level. The relative L2 error of the reconstructed flow field by FFPICN is reduced by about 30% compared to traditional PINNs and their variants.