Lagrangian representations of flow fields have gained prominence for enabling fast, accurate analysis and exploration of time-varying flow behaviors. In this paper, we present a comprehensive evaluation to establish a robust and efficient framework for Lagrangian-based particle tracing using deep neural networks (DNNs). Han et al. (2021) first proposed a DNN-based approach to learn Lagrangian representations and demonstrated accurate particle tracing for an analytic 2D flow field. In this paper, we extend and build upon this prior work in significant ways. First, we evaluate the performance of DNN models to accurately trace particles in various settings, including 2D and 3D time-varying flow fields, flow fields from multiple applications, flow fields with varying complexity, as well as structured and unstructured input data. Second, we conduct an empirical study to inform best practices with respect to particle tracing model architectures, activation functions, and training data structures. Third, we conduct a comparative evaluation of prior techniques that employ flow maps as input for exploratory flow visualization. Specifically, we compare our extended model against its predecessor by Han et al. (2021), as well as the conventional approach that uses triangulation and Barycentric coordinate interpolation. Finally, we consider the integration and adaptation of our particle tracing model with different viewers. We provide an interactive web-based visualization interface by leveraging the efficiencies of our framework, and perform high-fidelity interactive visualization by integrating it with an OSPRay-based viewer. Overall, our experiments demonstrate that using a trained DNN model to predict new particle trajectories requires a low memory footprint and results in rapid inference. Following best practices for large 3D datasets, our deep learning approach using GPUs for inference is shown to require approximately 46 times less memory while being more than 400 times faster than the conventional methods.

Abstract The computational work to perform particle advection‐based flow visualization techniques varies based on many factors, including number of particles, duration, and mesh type. In many cases, the total work is significant, and total execution time (“performance”) is a critical issue. This state‐of‐the‐art report considers existing optimizations for particle advection, using two high‐level categories: algorithmic optimizations and hardware efficiency. The sub‐categories for algorithmic optimizations include solvers, cell locators, I/O efficiency, and precomputation, while the sub‐categories for hardware efficiency all involve parallelism: shared‐memory, distributed‐memory, and hybrid. Finally, this STAR concludes by identifying current gaps in our understanding of particle advection performance and its optimizations.

Visualization and analysis of multivariate data and their uncertainty are top research challenges in data visualization. Constructing fiber surfaces is a popular technique for multivariate data visualization that generalizes the idea of level-set visualization for univariate data to multivariate data. In this paper, we present a statistical framework to quantify positional probabilities of fibers extracted from uncertain bivariate fields. Specifically, we extend the state-of-the-art Gaussian models of uncertainty for bivariate data to other parametric distributions (e.g., uniform and Epanechnikov) and more general nonparametric probability distributions (e.g., histograms and kernel density estimation) and derive corresponding spatial probabilities of fibers. In our proposed framework, we leverage Green's theorem for closed-form computation of fiber probabilities when bivariate data are assumed to have independent parametric and nonparametric noise. Additionally, we present a nonparametric approach combined with numerical integration to study the positional probability of fibers when bivariate data are assumed to have correlated noise. For uncertainty analysis, we visualize the derived probability volumes for fibers via volume rendering and extracting level sets based on probability thresholds. We present the utility of our proposed techniques via experiments on synthetic and simulation datasets.

Abstract Streamlines are an extensively utilized flow visualization technique for understanding, verifying, and exploring computational fluid dynamics simulations. One of the major challenges associated with the technique is selecting which streamlines to display. Using a large number of streamlines results in dense, cluttered visualizations, often containing redundant information and occluding important regions, whereas using a small number of streamlines could result in missing key features of the flow. Many solutions to select a representative set of streamlines have been proposed by researchers over the past two decades. In this state‐of‐the‐art report, we analyze and classify seed placement and streamline selection (SPSS) techniques used by the scientific flow visualization community. At a high‐level, we classify techniques into automatic and manual techniques, and further divide automatic techniques into three strategies: density‐based, feature‐based, and similarity‐based. Our analysis evaluates the identified strategy groups with respect to focus on regions of interest, minimization of redundancy, and overall computational performance. Finally, we consider the application contexts and tasks for which SPSS techniques are currently applied and have potential applications in the future.

Data reduction through compression is emerging as a promising approach to ease I/O costs for simulation codes on supercomputers. Typically, this compression is achieved by techniques that operate on individual time slices. However, as simulation codes advance in time, outputting multiple time slices as they go, the opportunity for compression incorporating the time dimension has not been extensively explored. Moreover, recent supercomputers are increasingly equipped with deeper memory hierarchies, including solid state drives and burst buffers, which creates the opportunity to temporarily store multiple time slices and then apply compression to them all at once, i.e., spatiotemporal compression. This paper explores the benefits of incorporating the time dimension into existing wavelet compression, including studying its key parameters and demonstrating its benefits in three axes: storage, accuracy, and temporal resolution. Our results demonstrate that temporal compression can improve each of these axes, and that the impact on performance for real systems, including tradeoffs in memory usage and execution time, is acceptable. We also demonstrate the benefits of spatiotemporal wavelet compression with real-world visualization use cases and tailored evaluation metrics.

To improve the reliability of on-chip network based systems, we design a deadlock-free routing technique that is more resilient to component failures and guarantees a higher degree of node connectivity. The routing methodology consists of three key steps. First, we determine the maximal connected subgraph of the faulty network by checking whether the defective components happen to be the cut vertices and bridges of the network topology. A precise fault diagnosis mechanism is used to identify partial defective routers. Second, we construct an acyclic channel dependency graph that breaks all cycles and preserves connectivity of the maximal connected subgraph. This is done through the cycle-breaking and connectivity guaranteed (CBCG) algorithm. Finally, we introduce a fault-tolerant adaptive routing scheme that can be used with or without virtual channels for network congestion avoidance and high-throughput routing. The simulation results show both the effectiveness and robustness of the proposed approach. For an 8 × 8 2D-Mesh with 40 percent of link damage, full connectivity and deadlock freedom are still archived without disabling any faultless router in 98.18 percent of the simulations. In a 2D-Torus, the simulation percentage is even higher (99.93 percent). The hardware overhead for supporting the introduced features is minimal. An on-line implementation of CBCG using TSMC 65nm library has only 0.966 and 1.139 percent area overhead for the 8 × 8 and 16 × 16 2D-Meshes.