Large-eddy simulation (LES) is one of the high-fidelity turbulence simulations by resolving large-scale motions while modeling the effects of unresolved subgrid scales. However, the predictive accuracy of LES is largely dependent on the subgrid-scale (SGS) model. Traditional SGS models, based on assumptions such as isotropy and scale similarity, have been successfully applied to canonical turbulent flows but often fail in complex flows. Recent advances in machine learning, especially neural network (NN), have opened a new paradigm for SGS modeling by learning complex, nonlinear relationships directly from high-fidelity data. In this paper, we review the limitations of traditional SGS models and examine the development of NN-based SGS models and their strengths and limitations. Toward universal NN-based SGS model development, we discuss critical issues related to extrapolation to high Reynolds numbers, generalization to untrained flows, physical consistency, and computational cost. By combining data-driven methods with physical intuition and principles, NN-based SGS modeling has the potential to enhance the fidelity and versatility of LES.

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• Turbulence
• Turbulence modeling
• Turbulence simulations