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 (ML) methods applied to parameter estimation, model identification, closure term reconstruction, and beyond, mostly from the perspective of large Eddy simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics, and the discretization is a key issue that needs to be considered for a successful ML‐augmented modeling strategy. In order to make the discussion useful for non‐experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self‐consistent manner. In this study, we present a survey of the current data‐driven model concepts and methods, highlight important developments, and put them into the context of the discussed challenges.

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In the present work, we explore the capability of artificial neural networks (ANN) to predict the closure terms for large eddy simulations (LES) solely from coarse-scale data. To this end, we derive a consistent framework for LES closure models, with special emphasis laid upon the incorporation of implicit discretization-based filters and numerical approximation errors. We investigate implicit filter types, which are inspired by the solution representation of discontinuous Galerkin and finite volume schemes and mimic the behaviour of the discretization operator, and a global Fourier cutoff filter as a representative of a typical explicit LES filter. Within the perfect LES framework, we compute the exact closure terms for the different LES filter functions from direct numerical simulation results of decaying homogeneous isotropic turbulence. Multiple ANN with a multilayer perceptron (MLP) or a gated recurrent unit (GRU) architecture are trained to predict the computed closure terms solely from coarse-scale input data. For the given application, the GRU architecture clearly outperforms the MLP networks in terms of accuracy, whilst reaching up to 99.9% cross-correlation between the networks' predictions and the exact closure terms for all considered filter functions. The GRU networks are also shown to generalize well across different LES filters and resolutions. The present study can thus be seen as a starting point for the investigation of data-based modeling approaches for LES, which not only include the physical closure terms, but account for the discretization effects in implicitly filtered LES as well.

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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 to parameter estimation, model identification, closure term reconstruction and beyond, mostly from the perspective of Large Eddy Simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics and the discretization is a key issue that needs to be considered for a successful ML-augmented modeling strategy. In order to make the discussion useful for non-experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self-consistent manner. Following, we present a survey of the current data-driven model concepts and methods, highlight important developments and put them into the context of the discussed challenges.