发表机构
Columbia University; Ergodic LLC（哥伦比亚大学; Ergodic有限责任公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出非线性动力学闭合替代线性Landau闭合，通过等变神经网络和Padé闭合在解析数据上训练，对bump-on-tail和slab ITG不稳定性将增长率误差降低三个数量级。
AI 中文摘要
Landau流体闭合在演化矩上是线性的。我们考察了放宽线性性的后果。作为示例，我们引入了非线性精确动力学响应闭合，该闭合在本征模上精确，但在叠加态上不精确。一个计数论证表明，对$N$个瞬时矩和场的闭合最多能表示$(N+1)/2$个叠加的本征模。在此指导下，我们在解析数据上训练了一个等变神经网络和一个学习的Padé闭合。对于bump-on-tail和slab ITG不稳定性，它们将增长率误差比Landau闭合降低了多达三个数量级。
英文摘要
Landau fluid closures are linear in the evolved moments. We examine the consequences of relaxing linearity. As an example, we introduce the nonlinear exact kinetic response closure, exact on an eigenmode but not on superpositions. A counting argument shows that a closure on $N$ instantaneous moments and the field can represent at most $(N+1)/2$ superposed eigenmodes. Guided by this, we train an equivariant neural-network and a learned Padé closure on analytic data. For bump-on-tail and slab ITG instabilities they reduce growth-rate errors by up to three orders of magnitude over Landau closures.
