静电等离子体中朗道阻尼的神经算子闭合模型
A Neural Operator Closure for Landau Damping in Electrostatic Plasma
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中文总结 AI 辅助
该研究提出用于一维静电等离子体朗道阻尼的非马尔可夫神经算子闭合模型，通过在线训练傅里叶神经算子，实现线性与非线性朗道阻尼的复现及泛化，且数值稳定。
中文摘要 AI 辅助
我们提出了一种数据驱动的等离子体流体闭合模型，用于处理一维线性和非线性静电朗道阻尼问题。在可微流体求解器中在线训练傅里叶神经算子（FNO），损失函数基于闭合流体模拟产生的轨迹计算，而非单个动力学快照。该闭合模型为非马尔可夫型，作用于已求解矩历史的滑动窗口，以表征未求解动力学的记忆效应。我们证明，以此方式训练的单个FNO可复现线性和非线性朗道阻尼，泛化至训练集之外的初始扰动振幅，并在独立流体模拟中保持数值稳定性。在非线性区域，学习到的热通量无需逐点匹配动力学热通量即可复现已求解矩的动力学，作为有效闭合模型补偿截断的高阶矩，尽管学习到的比通量预计依赖于数值格式和训练数据。对训练模型的敏感性分析表明，其计算出真实的矩-通量关系，且对记忆窗口的依赖具有物理结构。
英文摘要
We present a data-driven plasma fluid closure for both linear and nonlinear electrostatic Landau damping in one dimension. A Fourier Neural Operator (FNO) is trained online within a differentiable fluid solver, with the loss computed on trajectories produced by the closed fluid simulation rather than on individual kinetic snapshots. The closure is non-Markovian, acting on a trailing window of the resolved moment history so as to represent the memory of the unresolved dynamics. We demonstrate that a single FNO trained in this way reproduces both linear and nonlinear Landau damping, generalises to initial perturbation amplitudes outside the training set, and remains numerically stable when deployed in independent fluid simulations. In the nonlinear regime the learned heat flux reproduces the resolved-moment dynamics without matching the kinetic heat flux pointwise, behaving as an effective closure that compensates for the truncated higher moments, though the learned specific flux is expected to depend on the numerical scheme and training data. A sensitivity analysis of the trained model shows that it computes a genuine moment-to-flux relation whose reliance on the memory window is physically structured.
