Visitation Graphs: Interactive Ensemble Visualization with Visitation Maps

Modern applications in computational science are increasingly focusing on understanding uncertainty in models and parameters in simulations. In this paper, we describe visitation graphs, a novel approximation technique for the well-established visualization of steady 2D vector field ensembles using visitation maps. Our method allows the efficient and robust computation of arbitrary visitation maps for vector field ensembles. A pre-processing step that can be parallelized to a high degree eschews the needs to store every ensemble member and to re-calculate every time the start position of the visitation map is changed. Tradeoffs between accuracy of generated visitation maps on one side and pre-processing time and storage requirements on the other side can be made. Instead of downsampling ensemble members to a storable size, coarse visitation graphs can be stored, giving more accurate visitation maps while still reducing the amount of data. Thus accurate visitation map creation is possible for ensembles where the traditional visitation map creation is prohibitive. We describe our approach in detail and demonstrate its effectiveness and utility on examples from Computational Fluid Dynamics

Progressive Wasserstein Barycenters of Persistence Diagrams

This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables the computation of a persistence diagram which is representative of the set, and which visually conveys the number, data ranges and saliences of the main features of interest found in the set. Such representative diagrams are obtained by computing explicitly the discrete Wasserstein barycenter of the set of persistence diagrams, a notoriously computationally intensive task. In particular, we revisit efficient algorithms for Wasserstein distance approximation [12,51] to extend previous work on barycenter estimation [94]. We present a new fast algorithm, which progressively approximates the barycenter by iteratively increasing the computation accuracy as well as the number of persistent features in the output diagram. Such a progressivity drastically improves convergence in practice and allows to design an interruptible algorithm, capable of respecting computation time constraints. This enables the approximation of Wasserstein barycenters within interactive times. We present an application to ensemble clustering where we revisit the k-means algorithm to exploit our barycenters and compute, within execution time constraints, meaningful clusters of ensemble data along with their barycenter diagram. Extensive experiments on synthetic and real-life data sets report that our algorithm converges to barycenters that are qualitatively meaningful with regard to the applications, and quantitatively comparable to previous techniques, while offering an order of magnitude speedup when run until convergence (without time constraint). Our algorithm can be trivially parallelized to provide additional speedups in practice on standard workstations. [...

Visual Analysis of Variability and Features of Climate Simulation Ensembles

This PhD thesis is concerned with the visual analysis of time-dependent scalar field ensembles as occur in climate simulations. Modern climate projections consist of multiple simulation runs (ensemble members) that vary in parameter settings and/or initial values, which leads to variations in the resulting simulation data. The goal of ensemble simulations is to sample the space of possible futures under the given climate model and provide quantitative information about uncertainty in the results. The analysis of such data is challenging because apart from the spatiotemporal data, also variability has to be analyzed and communicated. This thesis presents novel techniques to analyze climate simulation ensembles visually. A central question is how the data can be aggregated under minimized information loss. To address this question, a key technique applied in several places in this work is clustering. The first part of the thesis addresses the challenge of finding clusters in the ensemble simulation data. Various distance metrics lend themselves for the comparison of scalar fields which are explored theoretically and practically. A visual analytics interface allows the user to interactively explore and compare multiple parameter settings for the clustering and investigate the resulting clusters, i.e. prototypical climate phenomena. A central contribution here is the development of design principles for analyzing variability in decadal climate simulations, which has lead to a visualization system centered around the new Clustering Timeline. This is a variant of a Sankey diagram that utilizes clustering results to communicate climatic states over time coupled with ensemble member agreement. It can reveal several interesting properties of the dataset, such as: into how many inherently similar groups the ensemble can be divided at any given time, whether the ensemble diverges in general, whether there are different phases in the time lapse, maybe periodicity, or outliers. The Clustering Timeline is also used to compare multiple climate simulation models and assess their performance. The Hierarchical Clustering Timeline is an advanced version of the above. It introduces the concept of a cluster hierarchy that may group the whole dataset down to the individual static scalar fields into clusters of various sizes and densities recording the nesting relationship between them. One more contribution of this work in terms of visualization research is, that ways are investigated how to practically utilize a hierarchical clustering of time-dependent scalar fields to analyze the data. To this end, a system of different views is proposed which are linked through various interaction possibilities. The main advantage of the system is that a dataset can now be inspected at an arbitrary level of detail without having to recompute a clustering with different parameters. Interesting branches of the simulation can be expanded to reveal smaller differences in critical clusters or folded to show only a coarse representation of the less interesting parts of the dataset. The last building block of the suit of visual analysis methods developed for this thesis aims at a robust, (largely) automatic detection and tracking of certain features in a scalar field ensemble. Techniques are presented that I found can identify and track super- and sub-levelsets. And I derive “centers of action” from these sets which mark the location of extremal climate phenomena that govern the weather (e.g. Icelandic Low and Azores High). The thesis also presents visual and quantitative techniques to evaluate the temporal change of the positions of these centers; such a displacement would be likely to manifest in changes in weather. In a preliminary analysis with my collaborators, we indeed observed changes in the loci of the centers of action in a simulation with increased greenhouse gas concentration as compared to pre-industrial concentration levels

Aerospace medicine and biology. A continuing bibliography with indexes, supplement 195

This bibliography lists 148 reports, articles, and other documents introduced into the NASA scientific and technical information system in June 1979

Curve boxplot: Generalization of boxplot for ensembles of curves

pre-printIn simulation science, computational scientists often study the behavior of their simulations by repeated solutions with variations in parameters and/or boundary values or initial conditions. Through such simulation ensembles, one can try to understand or quantify the variability or uncertainty in a solution as a function of the various inputs or model assumptions. In response to a growing interest in simulation ensembles, the visualization community has developed a suite of methods for allowing users to observe and understand the properties of these ensembles in an efficient and effective manner. An important aspect of visualizing simulations is the analysis of derived features, often represented as points, surfaces, or curves. In this paper, we present a novel, nonparametric method for summarizing ensembles of 2D and 3D curves. We propose an extension of a method from descriptive statistics, data depth, to curves. We also demonstrate a set of rendering and visualization strategies for showing rank statistics of an ensemble of curves, which is a generalization of traditional whisker plots or boxplots to multidimensional curves. Results are presented for applications in neuroimaging, hurricane forecasting and fluid dynamics

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

This paper presents a computational framework for the Principal Geodesic Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis (PCA) framework [87] to the Wasserstein metric space of merge trees [92]. We formulate MT-PGA computation as a constrained optimization problem, aiming at adjusting a basis of orthogonal geodesic axes, while minimizing a fitting energy. We introduce an efficient, iterative algorithm which exploits shared-memory parallelism, as well as an analytic expression of the fitting energy gradient, to ensure fast iterations. Our approach also trivially extends to extremum persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our approach - with MT-PGA computations in the orders of minutes for the largest examples. We show the utility of our contributions by extending to merge trees two typical PCA applications. First, we apply MT-PGA to data reduction and reliably compress merge trees by concisely representing them by their first coordinates in the MT-PGA basis. Second, we present a dimensionality reduction framework exploiting the first two directions of the MT-PGA basis to generate two-dimensional layouts of the ensemble. We augment these layouts with persistence correlation views, enabling global and local visual inspections of the feature variability in the ensemble. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a lightweight C++ implementation that can be used to reproduce our results

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

Assimilation of Historical Head Data to Estimate Spatial Distributions of Stream Bed and Aquifer Hydraulic Conductivity Fields

Management of water resources in alluvial aquifers relies mainly on understanding interactions between hydraulically connected streams and aquifers. Numerical models that simulate this interaction often are used as decision support tools in water resource management. However, the accuracy of numerical predictions relies heavily on the unknown system parameters (i.e. stream bed conductivity and aquifer hydraulic conductivity) which are spatially heterogeneous and difficult to measure directly. This paper employs an Ensemble Smoother to invert groundwater level measurements to jointly estimate spatially-varying streambed and alluvial aquifer hydraulic conductivity along a 35.6 km segment of the South Platte River in northeastern Colorado. The accuracy of the inversion procedure is evaluated using a synthetic experiment and historical groundwater level measurements, with the latter constituting the novelty of this study in the inversion and validation of high resolution fields of streambed and aquifer conductivities. Results show that the estimated streambed conductivity field and aquifer conductivity field produce an acceptable agreement between observed and simulated groundwater levels and stream flow rates. The estimated parameter fields are also used to simulate the spatially varying flow exchange between the alluvial aquifer and the stream, which exhibit high spatial variability along the river reach with a maximum average monthly aquifer gain of about 2.3 m3/day and a maximum average monthly aquifer loss of 2.8 m3/day, per unit area of streambed (m2). These results demonstrate that data assimilation inversion provides a reliable and computationally affordable tool to estimate the spatial variability of streambed and aquifer conductivities at high resolution in real-world systems

Ovis: A framework for visual analysis of ocean forecast ensembles

pre-printWe present a novel integrated visualization system that enables interactive visual analysis of ensemble simulations of the sea surface height that is used in ocean forecasting. The position of eddies can be derived directly from the sea surface height and our visualization approach enables their interactive exploration and analysis.The behavior of eddies is important in different application settings of which we present two in this paper. First, we show an application for interactive planning of placement as well as operation of off-shore structures using real-world ensemble simulation data of the Gulf of Mexico. Off-shore structures, such as those used for oil exploration, are vulnerable to hazards caused by eddies, and the oil and gas industry relies on ocean forecasts for efficient operations. We enable analysis of the spatial domain, as well as the temporal evolution, for planning the placement and operation of structures.Eddies are also important for marine life. They transport water over large distances and with it also heat and other physical properties as well as biological organisms. In the second application we present the usefulness of our tool, which could be used for planning the paths of autonomous underwater vehicles, so called gliders, for marine scientists to study simulation data of the largely unexplored Red Sea