Marina Evers

Given a time-varying scalar field, the analysis of correlations between different spatial regions, i.e., the linear dependence of time series within these regions, provides insights into the structural properties of the data. In this context, regions are connected components of the spatial domain with high time series correlations. The detection and analysis of such regions is often performed globally, which requires pairwise correlation computations that are quadratic in the number of spatial data samples. Thus, operations based on all pairwise correlations are computationally demanding, especially when dealing with ensembles that model the uncertainty in the spatio-temporal phenomena using multiple simulation runs. We propose a two-step procedure: In a first step, we map the spatial samples to a 3D embedding based on a pairwise correlation matrix computed from the ensemble of time series. The 3D embedding allows for a one-to-one mapping to a 3D color space such that the outcome can be visually investigated by rendering the colors for all samples in the spatial domain. In a second step, we generate a hierarchical image segmentation based on the color images. From then on, we can visually analyze correlations of regions at all levels in the hierarchy within an interactive setting, which includes the uncertainty-aware analysis of the region’s time series correlation and respective time lags.

Numerical simulations are commonly used to understand the parameter dependence of given spatio-temporal phenomena. Sampling a multi-dimensional parameter space and running the respective simulations leads to an ensemble of a large number of spatio-temporal simulation runs. A main objective for analyzing the ensemble is to partition (or segment) the multi-dimensional parameter space into connected regions of simulation runs with similar behavior. To facilitate such an analysis, we propose a novel visualization method for multi-dimensional parameter-space partitions. Our visualization is based on the concept of a hyper-slicer, which allows for undistorted views of the parameter-space segments’ extent and transitions. For navigation within the parameter space, interactions with a 2D embedding of the parameter-space samples, including their segment memberships, are supported. Parameter-space partitions are generated in a semi-automatic fashion by analyzing the similarity space of the ensemble’s simulation runs. Clusters of similar simulation runs induce the segments of the parameter-space partition. We link the parameter-space partitioning visualizations to similarity-space visualizations of the ensemble’s simulation runs and embed them into an interactive visual analysis tool that supports the analysis of all facets of the spatio-temporal simulation ensemble targeted at the overarching goal of analyzing the parameter-space partitioning. The partitioning can then be visually analyzed and interactively refined. We evaluated our approach with experts within case studies from three different domains.

Sensitivity analyses of simulation ensembles determine how simulation parameters influence the simulation’s outcome. Commonly, one global numerical sensitivity value is computed per simulation parameter. However, when considering 3D spatial simulations, the analysis of localized sensitivities in different spatial regions is of importance in many applications. For analyzing the spatial variation of parameter sensitivity, one needs to compute a spatial sensitivity scalar field per simulation parameter. Given n simulation parameters, we obtain multi-field data consisting of n scalar fields when considering all simulation parameters. We propose an interactive visual analytics solution to analyze the multi-field sensitivity data. It supports the investigation of how strongly and in what way individual parameters influence the simulation outcome, in which spatial regions this is happening, and what the interplay of the simulation parameters is. Its central component is an overview visualization of all sensitivity fields that avoids 3D occlusions by linearizing the data using an adapted scheme of data-driven space-filling curves. The spatial sensitivity values are visualized in a combination of a Horizon Graph and a line chart. We validate our approach by applying it to synthetic and real-world ensemble data.