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This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.
Most of the existing approaches to visualize vector field ensembles are to reveal the uncertainty of individual variables, for example, statistics, variability, etc. However, a user-defined derived feature like vortex or air mass is also quite significant, since they make more sense to domain scientists. In this paper, we present a new framework to extract user-defined derived features from different simulation runs. Specially, we use a detail-to-overview searching scheme to help extract vortex with a user-defined shape. We further compute the geometry information including the size, the geo-spatial location of the extracted vortexes. We also design some linked views to compare them between different runs. At last, the temporal information such as the occurrence time of the feature is further estimated and compared. Results show that our method is capable of extracting the features across different runs and comparing them spatially and temporally.
We propose a longest common subsequence (LCS) based approach to compute the distance among vector field ensembles. By measuring how many common blocks the ensemble pathlines passing through, the LCS distance defines the similarity among vector field ensembles by counting the number of sharing domain data blocks. Compared to the traditional methods (e.g. point-wise Euclidean distance or dynamic time warping distance), the proposed approach is robust to outlier, data missing, and sampling rate of pathline timestep. Taking the advantages of smaller and reusable intermediate output, visualization based on the proposed LCS approach revealing temporal trends in the data at low storage cost, and avoiding tracing pathlines repeatedly. Finally, we evaluate our method on both synthetic data and simulation data, which demonstrate the robustness of the proposed approach.
The objective of this work is to develop error-bounded lossy compression methods to preserve topological features in 2D and 3D vector fields. Specifically, we explore the preservation of critical points in piecewise linear vector fields. We define the preservation of critical points as, without any false positive, false negative, or false type change in the decompressed data, (1) keeping each critical point in its original cell and (2) retaining the type of each critical point (e.g., saddle and attracting node). The key to our method is to adapt a vertex-wise error bound for each grid point and to compress input data together with the error bound field using a modified lossy compressor. Our compression algorithm can be also embarrassingly parallelized for large data handling and in situ processing. We benchmark our method by comparing it with existing lossy compressors in terms of false positive/negative/type rates, compression ratio, and various vector field visualizations with several scientific applications.
Particle advection is an important vector field visualization technique that is difficult to apply to very large data sets in a distributed setting due to scalability limitations in existing algorithms. In this paper, we report on several experiments using work requesting dynamic scheduling which achieves balanced work distribution on arbitrary problems with minimal communication overhead. We present a corresponding prototype implementation, provide and analyze benchmark results, and compare our results to an existing algorithm.
Particle advection is the fundamental kernel behind most vector field visualization methods. Yet, the efficient parallel computation of large amounts of particle traces remains challenging. This is exacerbated by the variety of hardware trends in today's HPC arena, including increasing core counts in classical CPUs, many-core designs such as the Intel Xeon Phi, and massively parallel GPUs. The dedicated optimization of a particle advection kernel for each individual target architecture is both time-consuming and error prone. In this paper, we propose a performance-portable algorithm for particle advection. Our algorithm is based on the recently introduced VTK-m system and chiefly relies on its device adapter abstraction. We demonstrate the general portability of our implementation across a wide variety of hardware. Finally, our evaluation shows that our hardware-agnostic algorithm has comparable performance to hardware-specific algorithms.
This work focuses on visualizing uncertainty of local divergence of two-dimensional vector fields. Divergence is one of the fundamental attributes of fluid flows, as it can help domain scientists analyze potential positions of sources (positive divergence) and sinks (negative divergence) in the flow. However, uncertainty inherent in vector field data can lead to erroneous divergence computations, adversely impacting downstream analysis. While Monte Carlo (MC) sampling is a classical approach for estimating divergence uncertainty, it suffers from slow convergence and poor scalability with increasing data size and sample counts. Thus, we present a two-fold contribution that tackles the challenges of slow convergence and limited scalability of the MC approach. (1) We derive a closed-form approach for highly efficient and accurate uncertainty visualization of local divergence, assuming independently Gaussian-distributed vector uncertainties. (2) We further integrate our approach into Viskores, a platform-portable parallel library, to accelerate uncertainty visualization. In our results, we demonstrate significantly enhanced efficiency and accuracy of our serial analytical (speed-up up to 1946×) and parallel Viskores (speed-up up to 19698×) algorithms over the classical serial MC approach. We also demonstrate qualitative improvements of our probabilistic divergence visualizations over traditional mean-field visualization, which disregards uncertainty. We validate the accuracy and efficiency of our methods on wind forecast and ocean simulation datasets.
The surface line integral convolution(LIC) visualization technique produces dense visualization of vector fields on arbitrary surfaces. We present a screen space surface LIC algorithm for use in distributed memory data parallel sort last rendering infrastructures. The motivations for our work are to support analysis of datasets that are too large to fit in the main memory of a single computer and compatibility with prevalent parallel scientific visualization tools such as ParaView and VisIt. By working in screen space using OpenGL we can leverage the computational power of GPUs when they are available and run without them when they are not. We address efficiency and performance issues that arise from the transformation of data from physical to screen space by selecting an alternate screen space domain decomposition. We analyze the algorithm's scaling behavior with and without GPUs on two high performance computing systems using data from turbulent plasma simulations.
Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but also on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.
Abstract Critical point tracking is a core topic in scientific visualization for understanding the dynamic behaviour of time‐varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural stability of critical points, that is, the robustness of a critical point is the minimum amount of perturbation to the vector field necessary to cancel it. A theoretical basis has been established previously that relates critical point tracking with the notion of robustness, in particular, critical points could be tracked based on their closeness in stability, measured by robustness, instead of just distance proximity within the domain. However, in practice, the computation of classic robustness may produce artifacts when a critical point is close to the boundary of the domain; thus, we do not have a complete picture of the vector field behaviour within its local neighbourhood. To alleviate these issues, we introduce a multilevel robustness framework for the study of 2D time‐varying vector fields. We compute the robustness of critical points across varying neighbourhoods to capture the multiscale nature of the data and to mitigate the boundary effect suffered by the classic robustness computation. We demonstrate via experiments that such a new notion of robustness can be combined seamlessly with existing feature tracking algorithms to improve the visual interpretability of vector fields in terms of feature tracking, selection and comparison for large‐scale scientific simulations. We observe, for the first time, that the minimum multilevel robustness is highly correlated with physical quantities used by domain scientists in studying a real‐world tropical cyclone dataset. Such an observation helps to increase the physical interpretability of robustness.
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We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.
In search of novel, improved materials for magnetic data storage and spintronic devices, compounds that allow a tailoring of magnetic domain shapes and sizes are essential. Good candidates are materials with intrinsic anisotropies or competing interactions, as they are prone to host various domain phases that can be easily and precisely selected by external tuning parameters such as temperature and magnetic field. Here, we utilize vector magnetic fields to visualize directly the magnetic anisotropy in the uniaxial ferromagnet CeRu 2 Ga 2 B. We demonstrate a feasible control both globally and locally of domain shapes and sizes by the external field as well as a smooth transition from single stripe to bubble domains, which opens the door to future applications based on magnetic domain tailoring.
We describe a method for visualizing data flows on large networks. We transform data flow on fixed networks into a vector field, which can be directly visualized using scientific flow visualization techniques. We evaluated the method on power flowing through two transmission power networks: a small, regional, IEEE test system (RTS-96) and a large national-scale system (the Eastern Interconnection). For the larger and more complex transmission system, the method illustrates features of the power flow that are not accessible when visualizing the power transmission with traditional network visualization techniques.
Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. Here this paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual cluttering for visualizing 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures. Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely.
The International Commission on Illumination (CIE) designed its color space to be perceptually uniform so that a given numerical change in the color code corresponds to perceived change in color. This color encoding is demon- strated to be advantageous in scientific visualization and analysis of vector fields. The specific application is analysis of ice motion in the Arctic where patterns in smooth monthly-averaged ice motion are seen. Furthermore, fractures occurring in the ice cover result in discontinuities in the ice motion. This vector jump in displacement can also be visualized. We then analyze modeled and observed fractures through the use of a metric on the color space, and image amplitude and phase metrics. Amplitude and phase met- rics arise from image registration that is accomplished by sampling images using space filling curves, thus reducing the image registration problem to the more reliable functional alignment problem. We demonstrate this through an exploration of the metrics to compare model runs to an observed ice crack.
Vector field electron tomography (VFET) is extensively used for three-dimensional (3-D) imaging of magnetic materials at nanometer resolutions. The conventional approach is to reconstruct and visualize the magnetic vector potential or the magnetic field associated with the sample. There is a lack of algorithms capable of reconstructing the 3-D distribution of magnetization from VFET data. Unlike magnetic vector potential and magnetic field, magnetization is a fundamental physical property of the sample that does not extend beyond the dimensions of the sample. We present a model-based iterative reconstruction algorithm (MBIR) that reconstructs the magnetization by minimizing a cost function consisting of a forward model term and a prior model term. The forward model uses the physics of imaging to model the VFET data as a function of the magnetization, and the prior model enforces sparsity in the magnetization reconstruction. We then formulate an optimization algorithm based on the theory of alternate direction method of multipliers to minimize the resulting MBIR cost function. In conclusion, using simulated and real data, we show that our algorithm accurately reconstructs both the magnetization and the magnetic vector potential.
Abstract Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting) and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective “average event.” We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT’s capacities on a wave–mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass, which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article (Finkel et al. 2021) studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also backward in time to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the reactive current . The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions.