AI 中文总结
本研究提出结合本征正交分解（POD）与有效动力学生成学习（G-LED）的混合框架，实现高效湍流预测，对比三种配置验证其降阶后大幅降低计算成本且保留关键流动结构。
AI 中文摘要
预测湍流动力学需要在预测保真度与计算效率之间取得平衡。基于扩散的生成模型可表征复杂的时空动力学，但其应用于高维湍流流动时仍存在计算成本过高的问题。相比之下，本征正交分解（POD）能提供紧凑且物理解释明确的降阶表征，不过过度的模态截断会丢失相关流动结构。本研究提出一种混合降阶生成预测框架，将POD与有效动力学生成学习（G-LED）相结合。该方法在基于物理的模态空间中进行时间预测，再通过基于扩散的重构恢复具有物理意义的流场表征。研究采用圆柱绕流湍流尾迹的实验测量数据对该方法进行评估，对比了三种配置：全场G-LED、全局POD-G-LED和局域POD-G-LED。全场G-LED的保真度最高，能保留更丰富的涡量波动和更一致的湍动能分布，但扩散模型训练需约17小时，Transformer训练需7小时，预测100个未来快照需3分钟。通过将预测转移至降阶POD空间，全局POD-G-LED将上述成本分别降至约8小时、2小时和50秒，同时保留了主导的尾迹结构和相干高能结构。局域POD-G-LED公式为不同尾迹区域分配不同的模态分辨率，相较于全局降阶配置，其涡量统计和能量分布均得到改善。这些结果表明，将基于物理的模态表征与基于扩散的生成重构相结合，为高效湍流流动预测提供了有效途径。
英文摘要
Forecasting turbulent flow dynamics requires a balance between predictive fidelity and computational efficiency. Diffusion-based generative models can represent complex spatiotemporal dynamics, but their application to high-dimensional turbulent flows remains computationally expensive. In contrast, proper orthogonal decomposition (POD) provides compact, physically interpretable reduced-order representations, although aggressive modal truncation can remove relevant flow structures. This work introduces a hybrid reduced-order generative forecasting framework that combines POD with Generative Learning of Effective Dynamics (G-LED). The method performs temporal prediction in a physics-based modal space and uses diffusion-based reconstruction to recover physically meaningful flow-field representations. It is assessed using experimental measurements of the turbulent wake behind a circular cylinder. Three configurations are compared: full-field G-LED, global POD-G-LED, and localized POD-G-LED. Full-field G-LED provides the highest fidelity, preserving richer vorticity fluctuations and more consistent turbulent kinetic energy distributions, but requires approximately 17 h for diffusion-model training, 7 h for Transformer training, and 3 min to predict 100 future snapshots. By transferring prediction to a reduced POD space, global POD-G-LED reduces these costs to approximately 8 h, 2 h, and 50 s, respectively, while retaining dominant wake organization and coherent energetic structures. A localized POD-G-LED formulation assigns different modal resolutions to distinct wake regions and improves vorticity statistics and energetic distributions relative to the global reduced-order configuration. These results show that coupling physics-based modal representations with diffusion-based generative reconstruction offers an effective route to efficient turbulent-flow forecasting.
