Data compression is a powerful solution for addressing big data challenges in database and data management. In scientific data compression for vector fields, preserving topological information is essential for accurate analysis and visualization. The topological skeleton, a fundamental component of vector field topology, consists of critical points and their connectivity (i.e., separatrices). While previous work has focused on preserving critical points in error-controlled lossy compression, little attention has been given to preserving separatrices, which are equally important. In this work, we introduce TspSZ, an efficient error-bounded lossy compression framework designed to preserve both critical points and separatrices. Our key contributions are threefold. First, we propose TspSZ, a topological-skeleton-preserving lossy compression framework that integrates two algorithms, enabling existing critical-point-preserving compressors to also retain separatrices, significantly enhancing their topology preservation capabilities. Second, we optimize TspSZ for efficiency through tailored improvements and parallelization. Specifically, we introduce a new error control mechanism to achieve high compression ratios and implement a shared-memory parallelization strategy to boost compression throughput. Third, we evaluate TspSZ against state-of-the-art lossy and lossless compressors using four real-world scientific datasets. Experimental results show that TspSZ achieves compression ratios of up to 7.7× while effectively preserving the topological skeleton, ensuring efficient storage and transmission of scientific data without compromising topological integrity.

Error-bounded lossy compression has been widely adopted in many scientific domains because it can address the challenges in storing, transferring, and analyzing unprecedented amounts of scientific data. However, general error-bounded lossy compressors may fail to meet additional quality requirements for downstream analysis, a.k.a. Quantities of Interest (QoIs). This may lead to uncertainties and even misinterpretations in scientific discoveries, significantly limiting the use of lossy compression in practice. In this paper, we propose QPET, a novel, versatile, and portable framework for QoI-preserving error-bounded lossy compression, which overcomes the challenges of modeling diverse QoIs by leveraging numerical strategies. QPET features (1) high portability to multiple existing lossy compressors, (2) versatile preservation to most differentiable univariate and multivariate QoIs, and (3) significant compression improvements in QoI-preservation tasks. Experiments with six real-world datasets demonstrate that integrating QPET into state-of-the-art error-bounded lossy compressors can gain 2x to 10x compression speedups of existing QoI-preserving error-bounded lossy compression solutions, up to 1000% compression ratio improvements to general-purpose compressors, and up to 133% compression ratio improvements to existing QoI-integrated scientific 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 1.25 x and 4.38 x performance speedup in data writing and reading compared with the vanilla approach without compression.

Today's scientific simulations and instruments are producing a large amount of data, leading to difficulties in storing, transmitting, and analyzing these data. While error-controlled lossy compressors are effective in significantly reducing data volumes and efficiently developing databases for multiple scientific applications, they mainly support error controls on raw data, which leaves a significant gap between the data and user's downstream analysis. This may cause unqualified uncertainties in the outcomes of the analysis, a.k.a quantities of interest (QoIs), which are the major concerns of users in adopting lossy compression in practice. In this paper, we propose rigorous mathematical theories to preserve four families of QoIs that are widely used in scientific analysis during lossy compression along with practical implementations. Specifically, we first develop the error control theory for univariate QoIs which are essential for computing physical properties such as kinetic energy, followed by multivariate QoIs that are more commonly used in real-world applications. The proposed method is integrated into a state-of-the-art compression framework in a modular fashion, which could easily adapt to new QoIs and new compression algorithms. Experiments on real-world datasets demonstrate that the proposed method provides faithful error control on important QoIs including kinetic energy, regional average, and isosurface without trials and errors, while offering compression ratios that are up to 4X of the compression ratios provided by state-of-the-art compressors.