Para2Mesh: A dual diffusion framework for moving mesh adaptation

For decades, mesh quality has greatly influenced the accuracy and efficiency of computational fluid dynamics based on mesh discretization. For multi-scale feature problems in engineering design, a large number of simulations are usually required for similar geometries under certain conditions. The use of a fixed mesh for all design parameters does not guarantee that all critical physical features are captured in every case. The single-shot mesh adaptation methods offer a possible alternative, the relatively expensive implementation cost and the need for flow field information make them infeasible for practical applications. Although there are many researches attempting moving mesh adaptation, they are limited to the need for posteriori solution information during prediction. Overcoming this limitation is essential to improve computational accuracy and efficiency, and directly learning the mapping from design parameters to adaptive meshes is a more desirable research strategy.

Recently, a team led by Profs. Xuejun Liu and Hongqiang Lyu from Nanjing University of Aeronautics and Astronautics (NUAA) proposed for the first time an end-to-end dual-diffusion framework, Para2mesh, to achieve direct prediction from design parameters to adaptive meshes that are aligned with the flow field. This work not only realizes the complex nonlinear mapping from low-dimensional design parameters to high-dimensional initial flow fields or adaptive meshes, but also solves the inherent multi-scale problem in CFD.

The team published their work in Chinese Journal of Aeronautics (Vol. 38, Issue 7, 2025).

"Omitting the calculation of flow field posterior information in previous methods is a more efficient and desirable strategy for moving mesh adaption. The data-driven moving mesh adaption method proposed in this research integrates the entire adaptive process into a unified workflow, which generates high-quality adaptive meshes based on design parameters without resorting to any a posteriori solution information." said Xuejun Liu, a professor at the College of Artificial Intelligence, NUAA, whose research focuses on AI for Science.

Taking inspiration from thermodynamic diffusion and with the help of a denoising diffusion probabilistic model, the researchers gradually recovered the accurate initial flow field and adaptive mesh from the random noise in the two sub-networks. Specifically, the mesh moving adaptation framework contains two diffusion neural networks, namely the flow field diffusion network (FDN) and the mesh diffusion network (MDN).

The FDN reconstructs the full flow field using the design parameters as conditional information and serves as the mesh movement supervised information. In the MDN, the design parameters and flow field features extracted by the FDN are used to gradually deform the initial mesh until it is aligned with the flow field structure. The researchers interpreted the denoising process in MDN as a process of moving from a random mesh to an adaptive mesh. The two sub-networks ensure the alignment of the adaptive mesh with the physical features of the flow field by interacting feature information at the node level through customized mesh convolution.

"A series of typical computational fluid dynamics experiments demonstrate the generalization of the proposed method to different geometrical and physical features. This not only avoids the need for auxiliary equations and posterior information on the flow field, but also greatly improves the adaptive efficiency", said Prof. Lyu.

However, predicting the optimized adaptive mesh directly from the design parameters requires a large amount of training data, which requires comprehensive datasets to efficiently simulate complex flow. Currently, the proposed methods focus on mesh adaptation in specific domains where sufficient simulation data is available. Prof. Liu proposes future strategies that will be developed to mitigate these data requirements, thereby improving the adaptability and efficiency of the method in a more generalised fluid dynamics background.

Other contributors include Jian Yu and Ran Xu from the College of Artificial Intelligence, NUAA, Nanjing, China; Hongqiang Lyu and Wenxuan Ouyang from the College of Aeronautics, NUAA, Nanjing, China.

Original Source

Jian YU, Hongqiang LYU, Ran XU, Wenxuan OUYANG, Xuejun LIU. Para2Mesh: A dual diffusion framework for moving mesh adaptation [J]. Chinese Journal of Aeronautics, 2025, https://doi.org/10.1016/j.cja.2025.103441.

About Chinese Journal of Aeronautics 

Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering, monthly published by Elsevier. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice. CJA is indexed in SCI (IF = 5.7, Q1), EI, IAA, AJ, CSA, Scopus.