An efficient diffusion transformer-based method for reconstructing three-dimensional turbulent flows from two-dimensional observations

In the field of fluid mechanics, inferring high-dimensional data from low-dimensional observations enables the reconstruction of the high-dimensional flow field, allowing for a more comprehensive understanding of the flow, which is of great importance for analyzing flow mechanisms and optimizing aerodynamic designs. However, the lack of theoretical methodologies makes reconstructing three-dimensional (3D) flow fields a challenging task. To overcome this difficulty, a diffusion transformer-based method is proposed in this paper for reconstructing two-dimensional (2D) flow fields into 3D flow fields. The method introduces plane position embedding to enable reconstruction from arbitrary 2D planes, significantly enhancing flexibility. Furthermore, a local attention mechanism based on windows and planes is introduced to replace the vanilla global attention mechanism, improving computational efficiency by approximately 25%–40%. The developed method is applied to the reconstruction of several 3D turbulent flow fields both with and without objects. The results show that the diffusion transformer-based method in this paper exhibits high accuracy in flow field reconstruction for all numerical experiments compared to other methods such as U-Net and generative adversarial network-based approaches and achieves an average structural similarity index measure improvement of 20%, with normalized root mean square error improvements exceeding 50% in some test cases, and due to its lower resource consumption, the method demonstrates tremendous potential for reconstructing complex 3D fluid flows.