Direct Numerical Simulations (DNSs) of high Reynolds number turbulent flows, encountered in engineering, earth sciences, and astrophysics, are not tractable because of the curse of dimensionality associated with the number of degrees of freedom required to resolve all the dynamically significant spatio-temporal scales. Designing efficient and accurate Machine Learning (ML)-based reduced models of fluid turbulence has emerged recently as a promising approach to overcoming the curse of dimensionality challenge. However, to make the ML approaches reliable one needs to test their efficiency and accuracy, which is recognised as important but so far incomplete task. Aiming to improve this missing component of the promising approach, we design and evaluate two reduced models of 3D homogeneous isotropic turbulence and scalar turbulence based on state-of-the-art ML algorithms of the Deep Learning (DL) type: Convolutional Generative Adversarial Network (C-GAN) and Compressed Convolutional Long-Short-Term-Memory (CC-LSTM) Network. Quality and computational efficiency of the emulated velocity and scalar distributions is juxtaposed to the ground-truth DNS via physics-rich statistical tests. The reported results allow to uncover and classify weak and strong aspects of C-GAN and CC-LSTM. The reported results, as well as the physics-informed methodology developed to test the ML-based solutions, are expected to play a significant role in the future for making the DL schemes trustworthy through injecting and controlling missing physical information in computationally tractable ways.

中文翻译：

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具有物理信息诊断的 3D 湍流时空深度学习模型

工程、地球科学和天体物理学中遇到的高雷诺数湍流的直接数值模拟 (DNS) 难以处理，因为维数灾难与解析所有动态重要时空所需的自由度数相关秤。设计高效且准确的基于机器学习 (ML) 的流体湍流简化模型最近已成为克服维数挑战的一种很有前途的方法。然而，为了使 ML 方法可靠，需要测试它们的效率和准确性，这被认为是一项重要但迄今为止尚未完成的任务。旨在改进这个有前途的方法中缺失的部分，我们设计和评估基于深度学习 (DL) 类型的最先进 ML 算法的 3D 均匀各向同性湍流和标量湍流的两个简化模型：卷积生成对抗网络 (C-GAN) 和压缩卷积长短-Term-Memory (CC-LSTM) 网络。通过物理丰富的统计测试，仿真速度和标量分布的质量和计算效率与真实 DNS 并列。报告的结果允许发现和分类 C-GAN 和 CC-LSTM 的弱方面和强方面。报告的结果以及为测试基于 ML 的解决方案而开发的基于物理的方法，预计将在未来通过以计算上易于处理的方式注入和控制丢失的物理信息来使 DL 方案值得信赖，从而发挥重要作用。