Semi-Supervised Learning for High-Fidelity Fluid Flow Reconstruction

Physical simulations of fluids are crucial for understanding fluid dynamics across many applications, such as weather prediction and engineering design. While high-resolution numerical simulations can provide substantial accuracy in analysis, it also results in prohibitive computational costs. Conversely, lower-resolution simulations are computationally less expensive but compromise the accuracy and reliability of results. In this work, we propose a cascaded fluid reconstruction framework to combine large amounts of low-resolution and limited amounts of paired high-resolution direct simulations for accurate fluid analysis. Our method can improve the accuracy of simulations while preserving the efficiency of low-resolution simulations. Our framework involves a proposal network, pre-trained with small amounts of high-resolution labels, to reconstruct an initial high-resolution flow field. The field is then refined in the frequency domain to become more physically plausible using our proposed refinement network, known as ModeFormer, which is implemented as a complex-valued transformer, with physics-informed unsupervised training. Our experimental results demonstrate the effectiveness of our approach in enhancing the overall performance of fluid flow reconstruction. The code will be made publicly available at https://github.com/divelab/AIRS/tree/main/OpenPDE/CFRF.