参数增广曲线系综的视觉灵敏度分析
A Visual Sensitivity Analysis for Parameter-Augmented Ensembles of Curves
摘要：
工程师和计算科学家经常通过重复求解来研究他们的模拟行为，这些求解的参数可以是边界值或初始条件。通过这样的模拟集成，在一个解决方案中的不确定性作为各种输入参数的函数进行研究。数值模拟的解通常是时间函数、空间映射或时空输出。处理这种复杂输出的通常方法是将分析限制在时间/空间域中的几个探测器。这导致函数输出（曲线）及其相关输入参数的更小和更易于处理的集合：曲线的增强集合。本文描述了一个系统的交互式探索和分析，这样的增强合奏。通过主成分分析投影、核密度估计和高密度区域计算对功能输出进行描述性统计。这使得计算功能分位数和离群值成为可能。刷和连接系统的元素允许深入分析的合奏。该系统允许功能描述性统计，聚类检测，并最终通过蛛网图实现视觉灵敏度分析。我们提出了两个合成的例子，然后验证我们的方法在一个工业用例中使用水力求解器的海流研究。
英文摘要：
Engineers and computational scientists often study the behavior of their simulations by repeated solutions with variations in their parameters, which can be for instance boundary values or initial conditions. Through such simulation ensembles, uncertainty in a solution is studied as a function of the various input parameters. Solutions of numerical simulations are often temporal functions, spatial maps or spatio-temporal outputs. The usual way to deal with such complex outputs is to limit the analysis to several probes in the temporal/spatial domain. This leads to smaller and more tractable ensembles of functional outputs (curves) with their associated input parameters: augmented ensembles of curves. This article describes a system for the interactive exploration and analysis of such augmented ensembles. Descriptive statistics on the functional outputs are performed by Principal Component Analysis projection, kernel density estimation and the computation of High Density Regions. This makes possible the calculation of functional quantiles and outliers. Brushing and linking the elements of the system allows in-depth analysis of the ensemble. The system allows for functional descriptive statistics, cluster detection and finally for the realization of a visual sensitivity analysis via cobweb plots. We present two synthetic examples and then validate our approach in an industrial use-case concerning a marine current study using a hydraulic solver.
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