A recent study in turbulent flow simulation demonstrated the potential of
generative diffusion models for fast 3D surrogate modeling. This approach
eliminates the need for specifying initial states or performing lengthy
simulations, significantly accelerating the process. While adept at sampling
individual frames from the learned manifold of turbulent flow states, the
previous model lacks the capability to generate sequences, hindering analysis
of dynamic phenomena. This work addresses this limitation by introducing a 4D
generative diffusion model and a physics-informed guidance technique that
enables the generation of realistic sequences of flow states. Our findings
indicate that the proposed method can successfully sample entire subsequences
from the turbulent manifold, even though generalizing from individual frames to
sequences remains a challenging task. This advancement opens doors for the
application of generative modeling in analyzing the temporal evolution of
turbulent flows, providing valuable insights into their complex dynamics.

该研究介绍了一种生成扩散模型和物理引导技术，可以生成逼真的流动状态序列，从而实现对湍流流动的时间演变的分析，为生成建模在湍流动力学复杂性研究中提供了宝贵的见解。

时间展开：4D 湍流流动的生成建模

Unfolding Time: Generative Modeling for Turbulent Flows in 4D

Turbulent flow simulation plays a crucial role in various applications,
including aircraft and ship design, industrial process optimization, and
weather prediction. In this paper, we propose an advanced data-driven method
for simulating turbulent flow, representing a significant improvement over
existing approaches.
Our methodology combines the strengths of Video Prediction Transformer (VPTR)
(Ye & Bilodeau, 2022) and Multigrid Architecture (MgConv, MgResnet) (Ke et al.,
2017). VPTR excels in capturing complex spatiotemporal dependencies and
handling large input data, making it a promising choice for turbulent flow
prediction. Meanwhile, Multigrid Architecture utilizes multiple grids with
different resolutions to capture the multiscale nature of turbulent flows,
resulting in more accurate and efficient simulations.
Through our experiments, we demonstrate the effectiveness of our proposed
approach, named MGxTransformer, in accurately predicting velocity, temperature,
and turbulence intensity for incompressible turbulent flows across various
geometries and flow conditions. Our results exhibit superior accuracy compared
to other baselines, while maintaining computational efficiency.

采用数据驱动的方法，通过结合 Video Prediction Transformer 和 Multigrid Architecture，提出了一种名为 MGxTransformer 的新方法，用于对各种不可压湍流进行精确的速度、温度和湍流强度预测，结果表现出比其他基线更高的准确性和更高的计算效率。

多重网格记忆神经网络用于计算流体动力学

Neural Multigrid Memory For Computational Fluid Dynamics

A realistic inflow boundary condition is essential for successful simulation
of the developing turbulent boundary layer or channel flows. Recent advances in
artificial intelligence (AI) have enabled the development of an inflow
generator that performs better than the synthetic methods based on intuitions.
In the present work, we applied generative adversarial networks (GANs), a
representative of unsupervised learning, to generate an inlet boundary
condition of turbulent channel flow. Upon learning the two-dimensional spatial
structure of turbulence using data obtained from direct numerical simulation
(DNS) of turbulent channel flow, the GAN could generate instantaneous flow
fields that are statistically similar to those of DNS. Surprisingly, the GAN
could produce fields at various Reynolds numbers without any additional
simulation based on the trained data of only three Reynolds numbers. This
indicates that the GAN could learn the universal nature of Reynolds number
effect and might reflect other simulation conditions. Eventually, through a
combination of the GAN and a recurrent neural network (RNN), we developed a
novel model (RNN-GAN) that could generate time-varying fully developed flow for
a long time. The spatiotemporal correlations of the generated flow are in good
agreement with those of the DNS. This proves the usefulness of unsupervised
learning in the generation of synthetic turbulence fields.

本文利用生成对抗网络和循环神经网络结合的方式，通过无监督学习生成了一种可以模拟各种湍流雷诺数下流动的模拟数据，并与真实数据达成了一定程度上的拟合。