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Particle advection is one of the foundational algorithms for visualization and analysis and is central to understanding vector fields common to scientific simulations. Achieving efficient performance with large data in a distributed memory setting is notoriously difficult. Because of its simplicity and minimized movement of large vector field data, the Parallelize over Data (POD) algorithm has become a de facto standard. Despite its simplicity and ubiquitous usage, the scaling issues with the POD algorithm are known and have been described throughout the literature. In this paper, we describe a set of in-depth analyses of the POD algorithm that shed new light on the underlying causes for the poor performance of this algorithm. We designed a series of representative workloads to study the performance of the POD algorithm and executed them on a supercomputer while collecting timing and statistical data for analysis. We then performed two different types of analysis. In the first analysis, we introduce two novel metrics for measuring algorithmic efficiency over the course of a workload run. The second analysis was from the perspective of the particles being advected. Using particle centric analysis, we identify that the overheads associated with particle movement between processes (not the communication itself) have a dramatic impact on the overall execution time. In the first analysis, we introduce two novel metrics for measuring algorithmic efficiency over the course of a workload run. The second analysis was from the perspective of the particles being advected. Using particle-centric analysis, we identify that the overheads associated with particle movement between processes have a dramatic impact on the overall execution time. These overheads become particularly costly when flow features span multiple blocks, resulting in repeated particle circulation between blocks.

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly influences the memory use, run time, and accuracy of an uncertainty visualization algorithm. We use an entropy calculation directly on ensemble data to establish an expected result and then compare the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models. Our results verify that models matching the distribution of the ensemble indeed match the entropy. We further show that fewer bins in nonparametric histogram models are more effective whereas large numbers of bins in quantile models approach data accuracy.

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets., Comment: 9 pages paper + 2 page references, 8 figures, IEEE VIS 2024 paper to be published as a special issue of IEEE Transactions on Visualization and Computer Graphics (TVCG)

We introduce and evaluate a new algorithm for the in situ extraction of Lagrangian flow maps, which we call Boundary Termination Optimization (BTO). Our approach is a communication-free model, requiring no message passing or synchronization between processes, improving scalability, thereby reducing overall execution time and alleviating the encumbrance placed on simulation codes from in situ processing. We terminate particle integration at node boundaries and store only a subset of the flow map that would have been extracted by communicating particles across nodes, thus introducing an accuracy-performance tradeoff. We run experiments with as many as 2048 GPUs and with multiple simulation data sets. For the experiment configurations we consider, our findings demonstrate that our communication-free technique saves as much as 2x to 4x in execution time in situ, while staying nearly as accurate quantitatively and qualitatively as previous work. Most significantly, this study establishes the viability of approaching in situ Lagrangian flow map extraction using communication-free models in the future.