Harald Obermaier

Future Challenges for Ensemble Visualization

Simulating complex events is a challenge and often requires carefully selecting simulation parameters. As vast computation resources become available, researchers can run alternative parameter settings or simulation models in parallel, creating an ensemble of possible outcomes for a given event of interest. The visual analysis of ensembles is one of visualizations most important new areas and should greatly affect the field in the next few years. The goal is to develop expressive visualizations of an ensembles properties to support scientists in this demanding parameter-space exploration.

Comparative Visual Analysis of Lagrangian Transport in CFD Ensembles

Sets of simulation runs based on parameter and model variation, so-called ensembles, are increasingly used to model physical behaviors whose parameter space is too large or complex to be explored automatically. Visualization plays a key role in conveying important properties in ensembles, such as the degree to which members of the ensemble agree or disagree in their behavior. For ensembles of time-varying vector fields, there are numerous challenges for providing an expressive comparative visualization, among which is the requirement to relate the effect of individual flow divergence to joint transport characteristics of the ensemble. Yet, techniques developed for scalar ensembles are of little use in this context, as the notion of transport induced by a vector field cannot be modeled using such tools. We develop a Lagrangian framework for the comparison of flow fields in an ensemble. Our techniques evaluate individual and joint transport variance and introduce a classification space that facilitates incorporation of these properties into a common ensemble visualization. Variances of Lagrangian neighborhoods are computed using pathline integration and Principal Components Analysis. This allows for an inclusion of uncertainty measurements into the visualization and analysis approach. Our results demonstrate the usefulness and expressiveness of the presented method on several practical examples.

Characterizing and Visualizing Predictive Uncertainty in Numerical Ensembles Through Bayesian Model Averaging

Numerical ensemble forecasting is a powerful tool that drives many risk analysis efforts and decision making tasks. These ensembles are composed of individual simulations that each uniquely model a possible outcome for a common event of interest: e.g., the direction and force of a hurricane, or the path of travel and mortality rate of a pandemic. This paper presents a new visual strategy to help quantify and characterize a numerical ensembles predictive uncertainty: i.e., the ability for ensemble constituents to accurately and consistently predict an event of interest based on ground truth observations. Our strategy employs a Bayesian framework to first construct a statistical aggregate from the ensemble. We extend the information obtained from the aggregate with a visualization strategy that characterizes predictive uncertainty at two levels: at a global level, which assesses the ensemble as a whole, as well as a local level, which examines each of the ensembles constituents. Through this approach, modelers are able to better assess the predictive strengths and weaknesses of the ensemble as a whole, as well as individual models. We apply our method to two datasets to demonstrate its broad applicability.

Interpolation-Based Pathline Tracing in Particle-Based Flow Visualization

Particle tracing in time-varying flow fields is traditionally performed by numerical integration of the underlying vector field. This procedure can become computationally expensive, especially in scattered, particle-based flow fields, which complicate interpolation due to the lack of an explicit neighborhood structure. If such a particle-based flow field allows for the identification of consecutive particle positions, an alternative approach to particle tracing can be employed: we substitute repeated numerical integration of vector data by geometric interpolation in the highly dynamic particle system as defined by the particle-based simulation. To allow for efficient and accurate location and interpolation of changing particle neighborhoods, we develop a modified k-d tree representation that is capable of creating a dynamic partitioning of even highly compressible data sets with strongly varying particle densities. With this representation we are able to efficiently perform pathline computation by identifying, tracking, and updating an enclosing, dynamic particle neighborhood as particles move overtime. We investigate and evaluate the complexity, accuracy, and robustness of this interpolation-based alternative approach to trajectory generation in compressible and incompressible particle systems generated by simulation techniques such as Smoothed Particle Hydrodynamics (SPH).

Volume deformations in grid-less flow simulations

This paper presents a novel method for the extraction and visualization of volume deformations in grid‐less point based flow simulations. Our primary goals are the segmentation of different paths through a mixing device and the visualization of ellipsoidal particle deformations. The main challenges are the numerically efficient processing of deformation tensors and the robust integration of stream‐ and streaklines at boundaries of the dataset such that closed segments are obtained. Our results show two‐ and three‐dimensional particle deformations as well as the segmentation of volumes in stationary fields and areas in time‐dependent datasets taking consistent paths through a mixing device.

Derived Metric Tensors for Flow Surface Visualization

Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.

Cubic Gradient-Based Material Interfaces

Multifluid simulations often create volume fraction data, representing fluid volumes per region or cell of a fluid data set. Accurate and visually realistic extraction of fluid boundaries is a challenging and essential task for efficient analysis of multifluid data. In this work, we present a new material interface reconstruction method for such volume fraction data. Within each cell of the data set, our method utilizes a gradient field approximation based on trilinearly blended Coons-patches to generate a volume fraction function, representing the change in volume fractions over the cells. A continuously varying isovalue field is applied to this function to produce a smooth interface that preserves the given volume fractions well. Further, the method allows user-controlled balance between volume accuracy and physical plausibility of the interface. The method works on two- and three-dimensional Cartesian grids, and handles multiple materials. Calculations are performed locally and utilize only the one-ring of cells surrounding a given cell, allowing visualizations of the material interfaces to be easily generated on a GPU or in a large-scale distributed parallel environment. Our results demonstrate the robustness, accuracy, and flexibility of the developed algorithms.

A multi-resolution interpolation scheme for pathline based Lagrangian flow representations

Where the computation of particle trajectories in classic vector field representations includes computationally involved numerical integration, a Lagrangian representation in the form of a flow map opens up new alternative ways of trajectory extraction through interpolation. In our paper, we present a novel re-organization of the Lagrangian representation by sub-sampling a pre-computed set of trajectories into multiple levels of resolution, maintaining a bound over the amount of memory mapped by the file system. We exemplify the advantages of replacing integration with interpolation for particle trajectory calculation through a real-time, low memory cost, interactive exploration environment for the study of flow fields. Beginning with a base resolution, once an area of interest is located, additional trajectories from other levels of resolution are dynamically loaded, densely covering those regions of the flow field that are relevant for the extraction of the desired feature. We show that as more trajectories are loaded, the accuracy of the extracted features converges to the accuracy of the flow features extracted from numerical integration with the added benefit of real-time, non-iterative, multi-resolution path and time surface extraction.

Stream Volume Segmentation of Grid-Less Flow Simulation

We present a novel algorithm for the geometric extraction of stream volume segmentation for visualization of grid-less flow simulations. Our goal is the segmentation of different paths through a mixing tube where the flow is represented by scattered point sets approximated with moving least squares. The key challenges are thewatertight construction of boundary representations from separatrices. These are obtained by integrating and intersectingstream surfaces starting at separation and attachment lines at boundaries of flow obstacles. A major challenge is the robust integration of stream lines at boundaries with no-slip condition such that closed volume segments are obtained. Our results show the segmentation of volumes taking consistent paths through a mixing tube with six partitioning blades. Slicing these volumes provides valuable insight into the quality of the mixing process.

Modality-driven Classification and Visualization of Ensemble Variance.

Advances in computational power now enable domain scientists to address conceptual and parametric uncertainty by running simulations multiple times in order to sufficiently sample the uncertain input space. While this approach helps address conceptual and parametric uncertainties, the ensemble datasets produced by this technique present a special challenge to visualization researchers as the ensemble dataset records a distribution of possible values for each location in the domain. Contemporary visualization approaches that rely solely on summary statistics (e.g., mean and variance) cannot convey the detailed information encoded in ensemble distributions that are paramount to ensemble analysis; summary statistics provide no information about modality classification and modality persistence. To address this problem, we propose a novel technique that classifies high-variance locations based on the modality of the distribution of ensemble predictions. Additionally, we develop a set of confidence metrics to inform the end-user of the quality of fit between the distribution at a given location and its assigned class. Finally, for the special application of evaluating the stability of bimodal regions, we develop local and regional metrics.