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arXiv 2403.01532physics.plasm-phcs.LGphysics.comp-ph
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用于等离子体系统降阶建模的数据驱动局部算子发现：II. 在参数化动力学中的应用

Data-driven local operator finding for reduced-order modelling of plasma systems: II. Application to parametric dynamics

Imperial College London（帝国理工学院）；University of Washington（华盛顿大学）

Farbod Faraji, Maryam Reza, Aaron Knoll, J. Nathan Kutz

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24 pages, 17 figures
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AI总结：

本文扩展数据驱动局部算子发现算法 Phi Method，提出 parametric 与 ensemble 两种形式，用于参数化等离子体及流体动力学的 PDE 恢复与跨参数预测。

摘要：

现实世界系统的动力学往往受到各种固有或外部可控参数的影响，因此需要能够可靠捕捉这些参数化行为的模型。等离子体技术正是此类系统的典型例子。例如，支配 Hall thrusters（一种航天器推进技术）整体动力学的现象会随“自持电场”等多种参数而变化。在本第二部分中，继我们在第一部分提出新颖的数据驱动局部算子发现算法 Phi Method 之后，我们展示该方法在学习参数化动力学、以预测未见参数空间内系统行为方面的有效性。文中给出两种改进形式：“parametric Phi Method”和“ensemble Phi Method”，并通过二维圆柱绕流和一维 Hall-thruster 等离子体放电问题加以演示。在流体算例中与 parametric OPT-DMD 的对比评估表明，parametric Phi Method 具有更优的预测性能。在两个测试算例中，parametric Phi Method 与 ensemble Phi Method 均能可靠恢复支配性的参数化 PDE，并在测试参数上提供准确预测。Ensemble ROM 分析强调了 Phi Method 能够以高置信度稳健学习主导动力学系数。

英文摘要：

Real-world systems often exhibit dynamics influenced by various parameters, either inherent or externally controllable, necessitating models capable of reliably capturing these parametric behaviors. Plasma technologies exemplify such systems. For example, phenomena governing global dynamics in Hall thrusters (a spacecraft propulsion technology) vary with various parameters, such as the "self-sustained electric field". In this Part II, following on the introduction of our novel data-driven local operator finding algorithm, Phi Method, in Part I, we showcase the method's effectiveness in learning parametric dynamics to predict system behavior across unseen parameter spaces. We present two adaptations: the "parametric Phi Method" and the "ensemble Phi Method", which are demonstrated through 2D fluid-flow-past-a-cylinder and 1D Hall-thruster-plasma-discharge problems. Comparative evaluation against parametric OPT-DMD in the fluid case demonstrates superior predictive performance of the parametric Phi Method. Across both test cases, parametric and ensemble Phi Method reliably recover governing parametric PDEs and offer accurate predictions over test parameters. Ensemble ROM analysis underscores Phi Method's robust learning of dominant dynamic coefficients with high confidence.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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