用机器学习改进等离子体流体模拟的高阶闭合关系，提升对动能效应的捕捉能力。
The Machine Learning Approach to Moment Closure Relations for Plasma: A Review
- 采用神经网络与稀疏回归方法构建等离子体闭合模型
- 部分模型可在线模拟线性和非线性朗道阻尼现象
- 适合从事等离子体仿真与机器学习交叉研究者阅读
大规模全球等离子体模拟在空间与实验室等离子体物理中仍面临挑战。基于流体模型的任何模拟都需对高阶等离子体矩提供闭合关系。本文综述了近期机器学习方法在开发更优等离子体闭合模型方面的进展，这些模型能捕捉流体模型中的动能现象。我们梳理了两类方法：从多层感知机到傅里叶神经算子的神经网络代理模型（后者最近已在流体求解器中在线重现线性和非线性朗道阻尼），以及稀疏回归等方程发现方法；并按研究是否在离线参考数据上测试或在线集成于时间演化求解器进行组织。本文还指出机器学习闭合模型面临的挑战，包括非对角压强张量精度、超出训练分布的泛化能力，以及在大规模模拟中稳定集成的问题，并展望未来可能的研究方向。
原文摘要 · Abstract (English)
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.
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