A perspective on machine learning in turbulent flows

Unsupervised deep learning for super-resolution reconstruction of turbulence

“…Various deep-learning applications have recently been developed for broad areas of turbulence research (Kutz 2017; Brenner, Eldredge & Freund 2019; Duraisamy, Iaccarino & Xiao 2019; Brunton, Noack & Koumoutsakos 2020; Fukami, Fukagata & Taira 2020 a ; Pandey, Schumacher & Sreenivasan 2020). Ling, Kurzawski & Templeton (2016) proposed a tensor-based NN by embedding the Galilean invariance of a Reynolds-averaged Navier–Stokes (RANS) model, showing a greater performance improvement than linear and nonlinear eddy viscosity models.…”

Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models

“…The positive results from the machine learning models reinforce the importance of data-driven methods for modelling turbulence, a practice that is gaining popularity [46][47][48][49] . An accurate estimation of the large-scale velocity and heat transport helps scientists and engineers to better understand thermally driven flows encountered in nature and in engineering applications.…”

“…In this paper, we employ machine-learning (ML) tools to construct models for predicting Re and Nu. This approach, which is increasingly gaining popularity in fluid mechanics [46][47][48][49][50] , involves building and improving prediction algorithms by "learning" from the existing data [51][52][53] . Hence, in the present work, we do not delve much into the physics behind Re and Nu relations; instead, we use the data from previous works to develop the prediction models.…”

A perspective on machine learning methods in turbulence modeling

“…In this article, we intend to give an overview of recent research efforts into turbulence modeling with ML methods or, more precisely, data‐driven closure models and methods. It is not meant to replace the already existing valuable review articles on this matter, for example, [17,55,58], but to provide a complementary perspective with a particular focus on large Eddy simulation (LES) methods, although many of the challenges and chances of ML in this field also directly transfer to the Reynolds averaged Navier‐Stokes (RANS) system. We have attempted to present both the simulative side and the ML side in a concise and self‐contained manner with a focus on the basic principles, so that the text may be useful to nonspecialists as well, and provide a first starting point from which to venture further.…”