A Visual Sensitivity Analysis for Parameter-Augmented Ensembles of Curves

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 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 (PCA) 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.