Deep unsupervised learning of turbulence for inflow generation at various Reynolds numbers

Abstract

A B S T R A C TA 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.

Unsupervised deep learning for super-resolution reconstruction of turbulence

“…Good solutions should include transfer learning (Guastoni et al. 2020; Kim & Lee 2020 a ), data augmentation using symmetry, physics-informed NNs that impose constraints of governing equation (continuity or momentum equations) (Raissi, Perdikaris & Karniadakis 2019; Jiang et al. 2020), and physical constraints added to the NN (Mohan et al.…”

“…For example, it is possible to account for temporally successive data by adding a discriminator that considers temporal effects (Xie et al. 2018; Kim & Lee 2020 a ). Fifth, although in channel turbulence, we found 5.2 times extrapolation ability of our model in Reynolds number, we could not tell whether our model works well for the even higher Reynolds number.…”

“…For more practical and wider applications, a more generalized model that can be applied, even when paired data are not available, is needed. Kim & Lee (2020 a ) recently showed that unsupervised learning networks could generate turbulent flow fields for inflow boundary conditions from random initial seeds. This indeed demonstrates that a DNN can learn and reflect hidden similarities in unpaired turbulence.…”

“…Srinivasan et al (2019) predicted the temporal behaviour of simplified shear turbulence expressed as solutions of nine ordinary differential equations using a recurrent NN (RNN). Kim & Lee (2020a) proposed a high-resolution inflow turbulence generator at various Reynolds numbers, combining a generative adversarial network (GAN) and an RNN. As another noticeable attempt to apply machine learning to fluid dynamics, Raissi, Yazdani & Karniadakis (2020) reconstructed velocity and pressure fields from only visualizable concentration data based on a physics-informed NN framework.…”

Prediction of turbulent heat transfer using convolutional neural networks

“…As a remedy to this problem, unsupervised learning could be considered. Kim & Lee (2019) showed that it is possible to learn a similarity between simulations with different Reynolds numbers through unsupervised learning of turbulence. Likewise, connecting data from low-resolution and high-resolution simulations would be possible.…”