一种用于湍流数据压缩的物理信息矢量量化自编码器
A Physics-Informed Vector Quantized Autoencoder for Data Compression of Turbulent Flow
摘要：
分析来自湍流模拟的大规模数据是内存密集型的，需要大量资源。这一重大挑战凸显了对数据压缩技术的需求。在这项研究中，我们应用基于矢量量化的物理深度学习技术，从三维湍流模拟中生成离散的低维数据表示。深度学习框架由卷积层组成，并结合了对流的物理约束，例如保持速度梯度的不可压缩性和全局统计特性。使用统计、基于比较的相似性和基于物理的度量来评估模型的准确性。训练数据集由不可压缩、统计稳定、各向同性湍流的直接数值模拟产生。这种有损数据压缩方案的性能进行评估，不仅与看不见的数据从静止的，各向同性的湍流，但也与衰减的各向同性湍流的数据，和泰勒-格林涡流。将压缩比（CR）定义为原始数据大小与压缩数据大小之比，结果表明，我们的基于矢量量化的模型可以提供均方误差（MSE）为$O(10^{-3})$的CR $=85$，以及忠实地再现流的统计数据的预测，除了在非常小的尺度上有一些损失。与最近基于传统自动编码器的研究相比，在连续空间中进行压缩，我们的模型将CR提高了$30$ %以上，并将MSE降低了一个数量级。我们的压缩模型是一个有吸引力的解决方案的情况下，需要快速，高质量和低开销的编码和解码的大数据。
英文摘要：
Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients. The accuracy of the model is assessed using statistical, comparison-based similarity and physics-based metrics. The training data set is produced from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow. The performance of this lossy data compression scheme is evaluated not only with unseen data from the stationary, isotropic turbulent flow, but also with data from decaying isotropic turbulence, and a Taylor-Green vortex flow. Defining the compression ratio (CR) as the ratio of original data size to the compressed one, the results show that our model based on vector quantization can offer CR $=85$ with a mean square error (MSE) of $O(10^{-3})$, and predictions that faithfully reproduce the statistics of the flow, except at the very smallest scales where there is some loss. Compared to the recent study based on a conventional autoencoder where compression is performed in a continuous space, our model improves the CR by more than $30$ percent, and reduces the MSE by an order of magnitude. Our compression model is an attractive solution for situations where fast, high quality and low-overhead encoding and decoding of large data are required.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
