Spatio-temporal deep learning models of 3D turbulence with physics informed diagnostics

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.