The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics. Any simulation based on a fluid model inherently requires a closure relation for the high order plasma moments. This review compiles and analyses the recent surge of machine learning approaches developing improved plasma closure models capable of capturing kinetic phenomena within plasma fluid models. We survey two methodological families: neural-network surrogates (from multilayer perceptrons to Fourier neural operators, the latter recently reproducing both linear and non-linear Landau damping online within a fluid solver) and equation-discovery methods such as sparse regression; and organise the studies by whether they are tested offline against reference data or online within a time-evolving solver. We outline the challenges associated with machine-learning closures, including off-diagonal pressure-tensor accuracy, generalisation beyond the training distribution, and stable integration into large-scale simulations, and the directions future research might take to address them.

翻译：大规模等离子体全局模拟的需求是空间与实验室等离子体物理学中持续存在的挑战。基于流体模型的任何模拟都天然需要对高阶等离子体矩建立闭合关系。本综述汇编并分析了近期涌现的、旨在发展能够捕捉等离子体流体模型中动力学现象的改进型闭合模型的机器学习方法。我们考察了两类方法体系：神经网络代理模型（从多层感知机到傅里叶神经算子——后者近期已在流体求解器内实现了线性与非线性朗道阻尼的在线复现）以及方程发现方法（如稀疏回归）；并根据方法是否在离线条件下通过参考数据验证，或是在时间演化求解器中进行在线测试进行归类。我们阐述了机器学习闭合方法面临的挑战，包括非对角压强张量的精度、训练分布外泛化能力，以及在大规模模拟中的稳定集成问题，并指出了未来研究可能应对这些挑战的方向。