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Turbulence closure modeling using machine learning is at an early crossroads. The extraordinary success of machine learning (ML) in a variety of challenging fields has given rise to justifiable optimism regarding similar transformative…

This work presents a review of the current state of research in data-driven turbulence closure modeling. It offers a perspective on the challenges and open issues, but also on the advantages and promises of machine learning methods applied…

A recent thrust in turbulence closure modeling research is to incorporate machine learning (ML) elements, such as neural networks, for the purpose of enhancing the predictive capability to a broader class of flows. Such a turbulence closure…

Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…

Model extrapolation to unseen flow is one of the biggest challenges facing data-driven turbulence modeling, especially for models with high dimensional inputs that involve many flow features. In this study we review previous efforts on…

Machine-learning (ML) techniques provide a new and encouraging perspective for constructing turbulence models for Reynolds-averaged Navier--Stokes (RANS) simulations. In this study, an iterative ML-RANS computational framework is proposed…

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…

Turbulence remains one of the last unresolved problems of classical physics and a major bottleneck to accurate flow prediction in climate, aerospace, and energy systems. Industrial simulations therefore rely on averaged representations of…

This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS) and Large Eddy Simulation (LES) models of turbulent flows. Different approaches of…

The current revolution in the field of machine learning (ML) is leading to many interesting developments in a wide range of areas, including fluid mechanics. Here we review recent and emerging possibilities in the context of predictions,…

Turbulent flows play an important role in many scientific and technological design problems. Both Sub-Grid Scale (SGS) models in Large Eddy Simulations (LES) and Reynolds Averaged Navier Stokes (RANS) based modeling will require turbulence…

The application machine learning (ML) algorithms to turbulence modeling has shown promise over the last few years, but their application has been restricted to eddy viscosity based closure approaches. In this article we discuss rationale…

Fluid turbulence is an important problem for physics and engineering. Turbulence modeling deals with the development of simplified models that can act as surrogates for representing the effects of turbulence on flow evolution. Such models…

Generalizability of machine-learning (ML) based turbulence closures to accurately predict unseen practical flows remains an important challenge. At the Reynolds-averaged Navier-Stokes (RANS) level, NN-based turbulence closure modeling is…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSN), but current simulations must rely on subgrid models since direct numerical simulation (DNS) is too expensive. Unfortunately, existing…

Turbulent flows are of central importance across applications in science and engineering problems. For design and analysis, scientists and engineers use Computational Fluid Dynamics (CFD) simulations using turbulence models. Turbulent…

Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier--Stokes (RANS) equations. In the past few years, with the…

Computational Fluid Dynamics (CFD) simulations using turbulence models are commonly used in engineering design. Of the different turbulence modeling approaches that are available, eddy viscosity based models are the most common for their…

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…