标题： 用高斯过程回归量化平台轮廓测量的分辨率极限 显示英文标题

标题： Quantifying Resolution Limits in Pedestal Profile Measurements with Gaussian Process Regression

摘要： 边缘输运屏障（ETBs）在磁约束聚变等离子体中，通常称为台阶，对于实现高约束等离子体起着关键作用。 然而，它们的特征是在短长度尺度上等离子体压力急剧上升，这使得它们在实验上难以诊断。 在这项工作中，我们使用高斯过程回归（GPR）来开发基于第一性原理的度量标准，用于量化从实验测量中推断温度、压力或其他量的可微分剖面的空间和时间分辨率限制。 尽管我们专注于台阶，但这些方法是完全通用的，可以应用于任何涉及从离散测量中推断剖面的情况。 首先，我们将GPR与低通滤波建立对应关系，给出了与GPR引起的平滑相关的有效“截止频率”的显式表达式。 其次，我们引入了一个新的信息论度量，\(N_{eff}\)，它衡量对剖面或其导数的推断值有贡献的有效数据点数量。 这些度量使能够对“过拟合”和“过度正则化”之间的权衡进行定量评估，为GPR的使用者和消费者提供了一种系统的方法来评估推断剖面的可信度。 我们将这些工具应用于在静态和动态设置中使用GPR的实用建议，并展示了它们在利用DIII-D托卡马克的测量数据推断台阶剖面中的应用。 显示英文摘要

摘要： Edge transport barriers (ETBs) in magnetically confined fusion plasmas, commonly known as pedestals, play a crucial role in achieving high confinement plasmas. However, their defining characteristic, a steep rise in plasma pressure over short length scales, makes them challenging to diagnose experimentally. In this work, we use Gaussian Process Regression (GPR) to develop first-principles metrics for quantifying the spatiotemporal resolution limits of inferring differentiable profiles of temperature, pressure, or other quantities from experimental measurements. Although we focus on pedestals, the methods are fully general and can be applied to any setting involving the inference of profiles from discrete measurements. First, we establish a correspondence between GPR and low-pass filtering, giving an explicit expression for the effective `cutoff frequency' associated with smoothing incurred by GPR. Second, we introduce a novel information-theoretic metric, \(N_{eff}\), which measures the effective number of data points contributing to the inferred value of a profile or its derivative. These metrics enable a quantitative assessment of the trade-off between `over-fitting' and `over-regularization', providing both practitioners and consumers of GPR with a systematic way to evaluate the credibility of inferred profiles. We apply these tools to develop practical advice for using GPR in both time-independent and time-dependent settings, and demonstrate their usage on inferring pedestal profiles using measurements from the DIII-D tokamak.