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This research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the discrepancies in topology between original and decompressed datasets could potentially result in erroneous interpretations or even incorrect scientific conclusions. In this paper, we focus on preserving Morse-Smale segmentations in 2D/3D piecewise linear scalar fields, targeting the precise reconstruction of minimum/maximum labels induced by the integral line of each vertex. The key is to derive a series of edits during compression time; the edits are applied to the decompressed data, leading to an accurate reconstruction of segmentations while keeping the error within the prescribed error bound. To this end, we developed a workflow to fix extrema and integral lines alternatively until convergence within finite iterations; we accelerate each workflow component with shared-memory/GPU parallelism to make the performance practical for coupling with compressors. We demonstrate use cases with fluid dynamics, ocean, and cosmology application datasets with a significant acceleration with an NVIDIA A100 GPU. 

We explore an error‐bounded lossy compression approach for reducing scientific data associated with 2D/3D unstructured meshes. While existing lossy compressors offer a high compression ratio with bounded error for regular grid data, methodologies tailored for unstructured mesh data are lacking; for example, one can compress nodal data as 1D arrays, neglecting the spatial coherency of the mesh nodes. Inspired by the SZ compressor, which predicts and quantizes values in a multidimensional array, we dynamically reorganize nodal data into sequences. Each sequence starts with a seed cell; based on a predefined traversal order, the next cell is added to the sequence if the current cell can predict and quantize the nodal data in the next cell with the given error bound. As a result, one can efficiently compress the quantized nodal data in each sequence until all mesh nodes are traversed. This paper also introduces a suite of novel error metrics, namely continuous mean squared error (CMSE) and continuous peak signal‐to‐noise ratio (CPSNR), to assess compression results for unstructured mesh data. The continuous error metrics are defined by integrating the error function on all cells, providing objective statistics across nonuniformly distributed nodes/cells in the mesh. We evaluate our methods with several scientific simulations ranging from ocean‐climate models and computational fluid dynamics simulations with both traditional and continuous error metrics. We demonstrated superior compression ratios and quality than existing lossy compressors. 

Lossy compression has been employed to reduce the unprecedented amount of data produced by today's large-scale scientific simulations and high-resolution instruments. To avoid loss of critical information, state-of-the-art scientific lossy compressors provide error controls on relatively simple metrics such as absolute error bound. However, preserving these metrics does not translate to the preservation of topological features, such as critical points in vector fields. To address this problem, we investigate how to effectively preserve the sign of determinant in error-controlled lossy compression, as it is an important quantity of interest used for the robust detection of many topological features. Our contribution is three-fold. (1) We develop a generic theory to derive the allowable perturbation for one row of a matrix while preserving its sign of the determinant. As a practical use-case, we apply this theory to preserve critical points in vector fields because critical point detection can be reduced to the result of the point-in-simplex test that purely relies on the sign of determinants. (2) We optimize this algorithm with a speculative compression scheme to allow for high compression ratios and efficiently parallelize it in distributed environments. (3) We perform solid experiments with real-world datasets, demonstrating that our method achieves up to 440% improvements in compression ratios over state-of-the-art lossy compressors when all critical points need to be preserved. Using the parallelization strategies, our method delivers up to 1.25X and 4.38X performance speedup in data writing and reading compared with the vanilla approach without compression. 

Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this paper, we introduce TopoSZ, an error-bounded lossy compression method that preserves the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. The main idea is to derive topological constraints from contour-tree-induced segmentation from the data domain, and incorporate such constraints with a customized error-controlled quantization strategy from the SZ compressor (version 1.4). Our method allows users to control the pointwise error and the loss of topological features during the compression process with a global error bound and a persistence threshold. 

Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this paper, we introduce TopoSZ, an error-bounded lossy compression method that preserves the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. The main idea is to derive topological constraints from contour-tree-induced segmentation from the data domain, and incorporate such constraints with a customized error-controlled quantization strategy from the SZ compressor (version 1.4). Our method allows users to control the pointwise error and the loss of topological features during the compression process with a global error bound and a persistence threshold. 

Atmospheric rivers (ARs) are long, narrow regions of water vapor in the Earth's atmosphere that transport heat and moisture from the tropics to the mid‐latitudes. ARs are often associated with extreme weather events in North America and contribute significantly to water supply and flood risk. However, characterizing ARs has been a major challenge due to the lack of a universal definition and their structural variations. Existing AR detection tools (ARDTs) produce distinct AR boundaries for the same event, making the risk assessment of ARs a difficult task. Understanding these uncertainties is crucial to improving the predictability of AR impacts, including their landfall areas and associated precipitation, which could cause catastrophic flooding and landslides over the coastal regions. In this work, we develop an uncertainty visualization framework that captures boundary and interior uncertainties, i.e., structural variations, of an ensemble of ARs that arise from a set of ARDTs. We first provide a statistical overview of the AR boundaries using the contour boxplots of Whitaker et al. that highlight the structural variations of AR boundaries based on their nesting relationships. We then introduce the topological skeletons of ARs based on Morse complexes that characterize the interior variation of an ensemble of ARs. We propose an uncertainty visualization of these topological skeletons, inspired by MetroSets of Jacobson et al. that emphasizes the agreements and disagreements across the ensemble members. Through case studies and expert feedback, we demonstrate that the two approaches complement each other, and together they could facilitate an effective comparative analysis process and provide a more confident outlook on an AR's shape, area, and onshore impact.

 

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 and bilinear vector fields. We define the preservation of critical points as, without any false positive, false negative, or false type 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.