Visualization and Visual Analysis of Ensemble Data: A Survey

COMPO*SED: Composite Parallel Coordinates for Co-Dependent Multi-Attribute Choices

We propose Composite Parallel Coordinates, a novel parallel coordinates technique to effectively represent the interplay of component alternatives in a system. It builds upon a dedicated data model that formally describes the interaction of components. Parallel coordinates can help decision-makers identify the most preferred solution among a number of alternatives. Multi-component systems require one such multi-attribute choice for each component. Each of these choices might have side effects on the system's operability and performance, making them co-dependent. Common approaches employ complex multi-component models or involve back-and-forth iterations between single components until an acceptable compromise is reached. A simultaneous visual exploration across independently modeled but connected components is needed to make system design more efficient. Using dedicated layout and interaction strategies, our Composite Parallel Coordinates allow analysts to explore both individual properties of components as well as their interoperability and joint performance. We showcase the effectiveness of Composite Parallel Coordinates for co-dependent multi-attribute choices by means of three real-world scenarios from distinct application areas. In addition to the case studies, we reflect on observing two domain experts collaboratively working with the proposed technique and communicating along the way.

voxel2vec: A Natural Language Processing Approach to Learning Distributed Representations for Scientific Data

Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and ensemble data, are intricate and complex. This paper presents voxel2vec, a novel unsupervised representation learning model, which is used to learn distributed representations of scalar values/scalar-value combinations in a low-dimensional vector space. Its basic assumption is that if two scalar values/scalar-value combinations have similar contexts, they usually have high similarity in terms of features. By representing scalar values/scalar-value combinations as symbols, voxel2vec learns the similarity between them in the context of spatial distribution and then allows us to explore the overall association between volumes by transfer prediction. We demonstrate the usefulness and effectiveness of voxel2vec by comparing it with the isosurface similarity map of univariate data and applying the learned distributed representations to feature classification for multivariate data and to association analysis for time-varying and ensemble data.

Visual Parameter Space Exploration in Time and Space

Computational models, such as simulations, are central to a wide range of fields in science and industry. Those models take input parameters and produce some output. To fully exploit their utility, relations between parameters and outputs must be understood. These include, for example, which parameter setting produces the best result (optimization) or which ranges of parameter settings produce a wide variety of results (sensitivity). Such tasks are often difficult to achieve for various reasons, for example, the size of the parameter space, and supported with visual analytics. In this paper, we survey visual parameter space exploration (VPSE) systems involving spatial and temporal data. We focus on interactive visualizations and user interfaces. Through thematic analysis of the surveyed papers, we identify common workflow steps and approaches to support them. We also identify topics for future work that will help enable VPSE on a greater variety of computational models.

Graph Visualization: Alternative Models Inspired by Bioinformatics

Currently, the methods and means of human-machine interaction and visualization as its integral part are being increasingly developed. In various fields of scientific knowledge and technology, there is a need to find and select the most effective visualization models for various types of data, as well as to develop automation tools for the process of choosing the best visualization model for a specific case. There are many data visualization tools in various application fields, but at the same time, the main difficulty lies in presenting data of an interconnected (node-link) structure, i.e., networks. Typically, a lot of software means use graphs as the most straightforward and versatile models. To facilitate visual analysis, researchers are developing ways to arrange graph elements to make comparing, searching, and navigating data easier. However, in addition to graphs, there are many other visualization models that are less versatile but have the potential to expand the capabilities of the analyst and provide alternative solutions. In this work, we collected a variety of visualization models, which we call alternative models, to demonstrate how different concepts of information representation can be realized. We believe that adapting these models to improve the means of human-machine interaction will help analysts make significant progress in solving the problems researchers face when working with graphs.

EnConVis: A Unified Framework for Ensemble Contour Visualization

Ensemble simulation is a crucial method to handle potential uncertainty in modern simulation and has been widely applied in many disciplines. Many ensemble contour visualization methods have been introduced to facilitate ensemble data analysis. On the basis of deep exploration and summarization of existing techniques and domain requirements, we propose a unified framework of ensemble contour visualization, EnConVis (Ensemble Contour Visualization), which systematically combines state-of-the-art methods. We model ensemble contour visualization as a four-step pipeline consisting of four essential procedures: member filtering, point-wise modeling, uncertainty band extraction, and visual mapping. For each of the four essential procedures, we compare different methods they use, analyze their pros and cons, highlight research gaps, and attempt to fill them. Specifically, we add Kernel Density Estimation in the point-wise modeling procedure and multi-layer extraction in the uncertainty band extraction procedure. This step shows the ensemble data's details accurately and provides abstract levels. We also analyze existing methods from a global perspective. We investigate their mechanisms and compare their effects, on the basis of which, we offer selection guidelines for them. From the overall perspective of this framework, we find choices and combinations that have not been tried before, which can be well compensated by our method. Synthetic data and real-world data are leveraged to verify the efficacy of our method. Domain experts' feedback suggests that our approach helps them better understand ensemble data analysis.

Visualizing Ensemble Predictions of Music Mood

Music mood classification has been a challenging problem in comparison with other music classification problems (e.g., genre, composer, or period). One solution for addressing this challenge is to use an ensemble of machine learning models. In this paper, we show that visualization techniques can effectively convey the popular prediction as well as uncertainty at different music sections along the temporal axis while enabling the analysis of individual ML models in conjunction with their application to different musical data. In addition to the traditional visual designs, such as stacked line graph, ThemeRiver, and pixel-based visualization, we introduce a new variant of ThemeRiver, called "dual-flux ThemeRiver", which allows viewers to observe and measure the most popular prediction more easily than stacked line graph and ThemeRiver. Together with pixel-based visualization, dual-flux ThemeRiver plots can also assist in model-development workflows, in addition to annotating music using ensemble model predictions.

Development and Evaluation of Two Approaches of Visual Sensitivity Analysis to Support Epidemiological Modeling

Computational modeling is a commonly used technology in many scientific disciplines and has played a noticeable role in combating the COVID-19 pandemic. Modeling scientists conduct sensitivity analysis frequently to observe and monitor the behavior of a model during its development and deployment. The traditional algorithmic ranking of sensitivity of different parameters usually does not provide modeling scientists with sufficient information to understand the interactions between different parameters and model outputs, while modeling scientists need to observe a large number of model runs in order to gain actionable information for parameter optimization. To address the above challenge, we developed and compared two visual analytics approaches, namely: algorithm-centric and visualization-assisted, and visualization-centric and algorithm-assisted. We evaluated the two approaches based on a structured analysis of different tasks in visual sensitivity analysis as well as the feedback of domain experts. While the work was carried out in the context of epidemiological modeling, the two approaches developed in this work are directly applicable to a variety of modeling processes featuring time series outputs, and can be extended to work with models with other types of outputs.

Visual Analysis and Detection of Contrails in Aircraft Engine Simulations

Contrails are condensation trails generated from emitted particles by aircraft engines, which perturb Earth's radiation budget. Simulation modeling is used to interpret the formation and development of contrails. These simulations are computationally intensive and rely on high-performance computing solutions, and the contrail structures are not well defined. We propose a visual computing system to assist in defining contrails and their characteristics, as well as in the analysis of parameters for computer-generated aircraft engine simulations. The back-end of our system leverages a contrail-formation criterion and clustering methods to detect contrails' shape and evolution and identify similar simulation runs. The front-end system helps analyze contrails and their parameters across multiple simulation runs. The evaluation with domain experts shows this approach successfully aids in contrail data investigation.

S4: Self-Supervised Learning of Spatiotemporal Similarity

We introduce an ML-driven approach that enables interactive example-based queries for similar behavior in ensembles of spatiotemporal scientific data. This addresses an important use case in the visual exploration of simulation and experimental data, where data is often large, unlabeled and has no meaningful similarity measures available. We exploit the fact that nearby locations often exhibit similar behavior and train a Siamese Neural Network in a self-supervised fashion, learning an expressive latent space for spatiotemporal behavior. This space can be used to find similar behavior with just a few user-provided examples. We evaluate this approach on several ensemble datasets and compare with multiple existing methods, showing both qualitative and quantitative results.

Visual Analysis of Multi-Parameter Distributions Across Ensembles of 3D Fields

For an ensemble of 3D multi-parameter fields, we present a visual analytics workflow to analyse whether and which parts of a selected multi-parameter distribution is present in all ensemble members. Supported by a parallel coordinate plot, a multi-parameter brush is applied to all ensemble members to select data points with similar multi-parameter distribution. By a combination of spatial sub-division and a covariance analysis of partitioned sub-sets of data points, a tight partition in multi-parameter space with reduced number of selected data points is obtained. To assess the representativeness of the selected multi-parameter distribution across the ensemble, we propose a novel extension of violin plots that can show multiple parameter distributions simultaneously. We investigate the visual design that effectively conveys (dis-)similarities in multi-parameter distributions, and demonstrate that users can quickly comprehend parameter-specific differences regarding distribution shape and representativeness from a side-by-side view of these plots. In a 3D spatial view, users can analyse and compare the spatial distribution of selected data points in different ensemble members via interval-based isosurface raycasting. In two real-world application cases we show how our approach is used to analyse the multi-parameter distributions across an ensemble of 3D fields.

Technology Trends and Challenges for Large-Scale Scientific Visualization

Scientific visualization is a key approach to understanding the growing massive streams of data from scientific simulations and experiments. In this article, I review technology trends including the positive effects of Moore's law on science, the significant gap between processing and data storage speeds, the emergence of hardware accelerators for ray-tracing, and the availability of robust machine learning techniques. These trends represent changes to the status quo and present the scientific visualization community with a new set of challenges. A major challenge involves extending our approaches to visualize the modern scientific process, which includes scientific verification and validation. Another key challenge to the community is the growing number, size, and complexity of scientific datasets. A final challenge is to take advantage of emerging technology trends in custom hardware and machine learning to significantly improve the large-scale data visualization process.

Level of Detail Exploration of Electronic Transition Ensembles using Hierarchical Clustering

We present a pipeline for the interactive visual analysis and exploration of molecular electronic transition ensembles. Each ensemble member is specified by a molecular configuration, the charge transfer between two molecular states, and a set of physical properties. The pipeline is targeted towards theoretical chemists, supporting them in comparing and characterizing electronic transitions by combining automatic and interactive visual analysis. A quantitative feature vector characterizing the electron charge transfer serves as the basis for hierarchical clustering as well as for the visual representations. The interface for the visual exploration consists of four components. A dendrogram provides an overview of the ensemble. It is augmented with a level of detail glyph for each cluster. A scatterplot using dimensionality reduction provides a second visualization, highlighting ensemble outliers. Parallel coordinates show the correlation with physical parameters. A spatial representation of selected ensemble members supports an in‐depth inspection of transitions in a form that is familiar to chemists. All views are linked and can be used to filter and select ensemble members. The usefulness of the pipeline is shown in three different case studies.

GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations

We propose GNN-Surrogate, a graph neural network-based surrogate model to explore the parameter space of ocean climate simulations. Parameter space exploration is important for domain scientists to understand the influence of input parameters (e.g., wind stress) on the simulation output (e.g., temperature). The exploration requires scientists to exhaust the complicated parameter space by running a batch of computationally expensive simulations. Our approach improves the efficiency of parameter space exploration with a surrogate model that predicts the simulation outputs accurately and efficiently. Specifically, GNN-Surrogate predicts the output field with given simulation parameters so scientists can explore the simulation parameter space with visualizations from user-specified visual mappings. Moreover, our graph-based techniques are designed for unstructured meshes, making the exploration of simulation outputs on irregular grids efficient. For efficient training, we generate hierarchical graphs and use adaptive resolutions. We give quantitative and qualitative evaluations on the MPAS-Ocean simulation to demonstrate the effectiveness and efficiency of GNN-Surrogate. Source code is publicly available at https://github.com/trainsn/GNN-Surrogate.

Complex model calibration through emulation, a worked example for a stochastic epidemic model

Uncertainty quantification is a formal paradigm of statistical estimation that aims to account for all uncertainties inherent in the modelling process of real-world complex systems. The methods are directly applicable to stochastic models in epidemiology, however they have thus far not been widely used in this context. In this paper, we provide a tutorial on uncertainty quantification of stochastic epidemic models, aiming to facilitate the use of the uncertainty quantification paradigm for practitioners with other complex stochastic simulators of applied systems. We provide a formal workflow including the important decisions and considerations that need to be taken, and illustrate the methods over a simple stochastic epidemic model of UK SARS-CoV-2 transmission and patient outcome. We also present new approaches to visualisation of outputs from sensitivity analyses and uncertainty quantification more generally in high input and/or output dimensions.

DLA-VPS: Deep-Learning-Assisted Visual Parameter Space Analysis of Cosmological Simulations

Cosmologists often build a mathematics simulation model to study the observed universe. However, running a high-fidelity simulation is time consuming and thus can inconvenience the analysis. This is especially so when the analysis involves trying out a large number of simulation input parameter configurations. Therefore, selecting an input parameter configuration that can meet the needs of an analysis task has become an important part of the analysis process. In this work, we propose an interactive visual system that efficiently helps users understand the parameter space related to their cosmological data. Our system utilizes a GAN-based surrogate model to reconstruct the simulation outputs without running the expensive simulation. We also extract information learned by the deep neural-network-based surrogate models to facilitate the parameter space exploration. We demonstrate the effectiveness of our system via multiple case studies. These case study results demonstrate valuable simulation input parameter configuration and subregion analyses.

Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of scalar fields. Data uncertainty inherent to scalar fields due to randomness in their acquisition and processing, however, limits our understanding of Morse complexes as structural abstractions. We, therefore, explore uncertainty visualization of an ensemble of 2D Morse complexes that arises from scalar fields coupled with data uncertainty. We propose several statistical summary maps as new entities for quantifying structural variations and visualizing positional uncertainties of Morse complexes in ensembles. Specifically, we introduce three types of statistical summary maps - the probabilistic map, the significance map, and the survival map - to characterize the uncertain behaviors of gradient flows. We demonstrate the utility of our proposed approach using wind, flow, and ocean eddy simulation datasets.

Uncertainty Visualization: Concepts, Methods, and Applications in Biological Data Visualization

This paper provides an overview of uncertainty visualization in general, along with specific examples of applications in bioinformatics. Starting from a processing and interaction pipeline of visualization, components are discussed that are relevant for handling and visualizing uncertainty introduced with the original data and at later stages in the pipeline, which shows the importance of making the stages of the pipeline aware of uncertainty and allowing them to propagate uncertainty. We detail concepts and methods for visual mappings of uncertainty, distinguishing between explicit and implict representations of distributions, different ways to show summary statistics, and combined or hybrid visualizations. The basic concepts are illustrated for several examples of graph visualization under uncertainty. Finally, this review paper discusses implications for the visualization of biological data and future research directions.

EPIsembleVis: A geo-visual analysis and comparison of the prediction ensembles of multiple COVID-19 models

We present EPIsembleVis, a web-based comparative visual analysis tool for evaluating the consistency of multiple COVID-19 prediction models. Our approach analyzes a collection of COVID-19 predictions from different epidemiological models as an ensemble and utilizes two metrics to quantify model performance. These metrics include (a) prediction uncertainty (represented as the dispersion of predictions in each ensemble) and (b) prediction error (calculated by comparing individual model predictions with the recorded data). Through an interactive visual interface, our approach provides a data-driven workflow for (a) selecting and constructing the COVID-19 model prediction ensemble based on the spatiotemporal overlap of available predictions of multiple epidemiological models, (b) quantifying the model performance using both the uncertainty of each model prediction ensemble, and the error of each ensemble member that represents individual model predictions, and (c) visualizing the spatiotemporal variability in the projection performance of individual models using a suite of novel ensemble visualization techniques, such as the data availability map, a spatiotemporal textured-tile calendar, multivariate rose chart, and time-series leaflet glyph. We demonstrate the capability of our ensemble visual interface through a case study that investigates the performance of weekly COVID-19 predictions, which are provided through the COVID-19 Forecast Hub UMass-Amherst Influenza Forecasting Center of Excellence [47] for the United States and United States Territories. The EPIsembleVis tool is implemented using open-source web technologies and adaptive system design, rendering it interoperable with Elasticsearch and Kibana for automatically ingesting COVID-19 predictions from online repositories, and it is generalizable for analyzing worldwide projections from more epidemiological models.

SpotSDC: Revealing the Silent Data Corruption Propagation in High-Performance Computing Systems

The trend of rapid technology scaling is expected to make the hardware of high-performance computing (HPC) systems more susceptible to computational errors due to random bit flips. Some bit flips may cause a program to crash or have a minimal effect on the output, but others may lead to silent data corruption (SDC), i.e., undetected yet significant output errors. Classical fault injection analysis methods employ uniform sampling of random bit flips during program execution to derive a statistical resiliency profile. However, summarizing such fault injection result with sufficient detail is difficult, and understanding the behavior of the fault-corrupted program is still a challenge. In this article, we introduce SpotSDC, a visualization system to facilitate the analysis of a program's resilience to SDC. SpotSDC provides multiple perspectives at various levels of detail of the impact on the output relative to where in the source code the flipped bit occurs, which bit is flipped, and when during the execution it happens. SpotSDC also enables users to study the code protection and provide new insights to understand the behavior of a fault-injected program. Based on lessons learned, we demonstrate how what we found can improve the fault injection campaign method.

The energy distance for ensemble and scenario reduction

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but are also used in probabilistic forecasting, clustering and estimating generative adversarial networks. We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy. We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data-based examples for electricity demand profiles and day-ahead electricity prices. This article is part of the theme issue 'The mathematics of energy systems'.

Uncertainty-Oriented Ensemble Data Visualization and Exploration using Variable Spatial Spreading

As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines. Visualization is a promising and powerful ensemble simulation analysis method. However, conventional visualization methods mainly aim at data simplification and highlighting important information based on domain expertise instead of providing a flexible data exploration and intervention mechanism. Trial-and-error procedures have to be repeatedly conducted by such approaches. To resolve this issue, we propose a new perspective of ensemble data analysis using the attribute variable dimension as the primary analysis dimension. Particularly, we propose a variable uncertainty calculation method based on variable spatial spreading. Based on this method, we design an interactive ensemble analysis framework that provides a flexible interactive exploration of the ensemble data. Particularly, the proposed spreading curve view, the region stability heat map view, and the temporal analysis view, together with the commonly used 2D map view, jointly support uncertainty distribution perception, region selection, and temporal analysis, as well as other analysis requirements. We verify our approach by analyzing a real-world ensemble simulation dataset. Feedback collected from domain experts confirms the efficacy of our framework.

Information Guided Exploration of Scalar Values and Isocontours in Ensemble Datasets

Uncertainty of scalar values in an ensemble dataset is often represented by the collection of their corresponding isocontours. Various techniques such as contour-boxplot, contour variability plot, glyphs and probabilistic marching-cubes have been proposed to analyze and visualize ensemble isocontours. All these techniques assume that a scalar value of interest is already known to the user. Not much work has been done in guiding users to select the scalar values for such uncertainty analysis. Moreover, analyzing and visualizing a large collection of ensemble isocontours for a selected scalar value has its own challenges. Interpreting the visualizations of such large collections of isocontours is also a difficult task. In this work, we propose a new information-theoretic approach towards addressing these issues. Using specific information measures that estimate the predictability and surprise of specific scalar values, we evaluate the overall uncertainty associated with all the scalar values in an ensemble system. This helps the scientist to understand the effects of uncertainty on different data features. To understand in finer details the contribution of individual members towards the uncertainty of the ensemble isocontours of a selected scalar value, we propose a conditional entropy based algorithm to quantify the individual contributions. This can help simplify analysis and visualization for systems with more members by identifying the members contributing the most towards overall uncertainty. We demonstrate the efficacy of our method by applying it on real-world datasets from material sciences, weather forecasting and ocean simulation experiments.