国防科技大学冷洪泽团队近日实现了基于增强扩散模型和傅里叶神经算子的物理场超分辨率重建。2025年6月17日，《理论与应用力学快报》发表了这一成果。

随着计算科学和工程领域对高精度流场模拟的需求不断增长，物理场的超分辨率重建引起了相当大的研究兴趣。然而，传统的数值方法通常需要高昂的计算成本，涉及复杂的数据处理，并且难以捕捉精细尺度的高频细节。为了应对这些挑战，研究组提出了一种创新的超分辨率重建框架，该框架将傅里叶神经算子（FNO）与增强的扩散模型相结合。该框架采用自适应加权FNO来处理低分辨率流场输入，有效地捕获全局相关性和高频特征。 

此外，引入残差引导扩散模型以进一步提高重建性能。该模型使用马尔可夫链将高分辨率场映射到低分辨率场，并结合了由自适应时间步长常微分方程（ODE）求解器求解的反向扩散过程，确保了稳定性和计算效率。实验结果表明，所提出的框架在准确性和效率方面明显优于现有方法，为科学模拟中的细粒度数据重建提供了一种有前景的解决方案。

附：英文原文

Title: Physics Field Super-resolution Reconstruction via Enhanced Diffusion Model and Fourier Neural Operator

Author: Yanan Guo, Junqiang Song, Xiaoqun Cao, Chuanfeng Zhao, Hongze Leng

Issue&Volume: 2025-06-17

Abstract: With the growing demand for high-precision flow field simulations in computational science and engineering, the super-resolution reconstruction of physical fields has attracted considerable research interest. However, traditional numerical methods often entail high computational costs, involve complex data processing, and struggle to capture fine-scale high-frequency details. To address these challenges, we propose an innovative super-resolution reconstruction framework that integrates a Fourier neural operator (FNO) with an enhanced diffusion model. The framework employs an adaptively weighted FNO to process low-resolution flow field inputs, effectively capturing global dependencies and high-frequency features. Furthermore, a residualguided diffusion model is introduced to further improve reconstruction performance. This model uses a Markov chain to map high-resolution fields to low-resolution counterparts and incorporates a reverse diffusion process solved by an adaptive time-step ordinary differential equation (ODE) solver, ensuring both stability and computational efficiency. Experimental results demonstrate that the proposed framework significantly outperforms existing methods in terms of accuracy and efficiency, offering a promising solution for fine-grained data reconstruction in scientific simulations.

DOI: 10.1016/j.taml.2025.100604

Source: http://taml.cstam.org.cn/article/doi/10.1016/j.taml.2025.100604pageType=en