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Scientific simulations and observations are generating massive volumes of time-varying vector field data, posing significant challenges for long-term storage and data transmission. Lossy compression is widely regarded as a promising approach for reducing data volume, as lossless methods typically achieve only modest compression ratios and therefore provide limited reduction. However, directly applying existing lossy compression techniques to time-varying vector fields can introduce undesirable distortions in critical-point trajectories, which encode essential structural properties of the underlying field. In this work, we present an efficient lossy compression framework that exactly preserves all critical-point trajectories in time-varying vector fields. Our contributions are threefold. First, we extend the theory of critical-point preservation from the spatial domain to space-time and develop a corresponding compression framework to guarantee trajectory preservation. Second, we introduce a semi-Lagrangian predictor to more effectively exploit spatiotemporal correlations in advection-dominated regions, and integrate it with the classical Lorenzo predictor to further improve compression efficiency. Third, we evaluate the proposed approach against state-of-the-art lossy and lossless compressors on four real-world scientific datasets. Experimental results show that our method achieves compression ratios of up to 124.48X while effectively preserving all critical-point trajectories. This compression ratio is up to 56.07X higher than the best-performing lossless compressors. In contrast, none of the existing lossy compressors can preserve all critical-point trajectories at comparable compression ratios. 

Scientific simulations and observations are generating massive volumes of time-varying vector field data, posing significant challenges for long-term storage and data transmission. Lossy compression is widely regarded as a promising approach for reducing data volume, as lossless methods typically achieve only modest compression ratios and therefore provide limited reduction. However, directly applying existing lossy compression techniques to time-varying vector fields can introduce undesirable distortions in critical-point trajectories, which encode essential structural properties of the underlying field. In this work, we present an efficient lossy compression framework that exactly preserves all critical-point trajectories in time-varying vector fields. Our contributions are threefold. First, we extend the theory of critical-point preservation from the spatial domain to space-time and develop a corresponding compression framework to guarantee trajectory preservation. Second, we introduce a semi-Lagrangian predictor to more effectively exploit spatiotemporal correlations in advection-dominated regions, and integrate it with the classical Lorenzo predictor to further improve compression efficiency. Third, we evaluate the proposed approach against state-of-the-art lossy and lossless compressors on four real-world scientific datasets. Experimental results show that our method achieves compression ratios of up to 124.48X while effectively preserving all critical-point trajectories. This compression ratio is up to 56.07X higher than the best-performing lossless compressors. In contrast, none of the existing lossy compressors can preserve all critical-point trajectories at comparable compression ratios. 

Lossy compression, widely used by scientists to reduce data from simulations, experiments, and observations, can distort features of interest even under bounded error. Such distortions may compromise downstream analyses and lead to incorrect scientific conclusions in applications such as combustion and cosmology. This paper presents a distributed and parallel algorithm for correcting topological features, specifically, piecewise linear Morse–Smale segmentations (PLMSS), which decompose the domain into monotone regions labeled by their corresponding local minima and maxima. While a single-GPU algorithm (MSz) exists for PLMSS correction after compression, no methodology has been developed that scales beyond a single GPU for extreme-scale data. We identify the key bottleneck in scaling PLMSS correction as the parallel computation of integral paths, a communication-intensive computation that is notoriously difficult to scale. Instead of explicitly computing and correcting integral paths, our algorithm simplifies MSz by preserving steepest ascending and descending directions across all locations, thereby minimizing interprocess communication while introducing negligible additional storage overhead. With this simplified algorithm and relaxed synchronization, our method achieves over 90% parallel efficiency on 128 GPUs on the Perlmutter supercomputer for real-world datasets. 

Lossy compression, widely used by scientists to reduce data from simulations, experiments, and observations, can distort features of interest even under bounded error. Such distortions may compromise downstream analyses and lead to incorrect scientific conclusions in applications such as combustion and cosmology. This paper presents a distributed and parallel algorithm for correcting topological features, specifically, piecewise linear Morse–Smale segmentations (PLMSS), which decompose the domain into monotone regions labeled by their corresponding local minima and maxima. While a single-GPU algorithm (MSz) exists for PLMSS correction after compression, no methodology has been developed that scales beyond a single GPU for extreme-scale data. We identify the key bottleneck in scaling PLMSS correction as the parallel computation of integral paths, a communication-intensive computation that is notoriously difficult to scale. Instead of explicitly computing and correcting integral paths, our algorithm simplifies MSz by preserving steepest ascending and descending directions across all locations, thereby minimizing interprocess communication while introducing negligible additional storage overhead. With this simplified algorithm and relaxed synchronization, our method achieves over 90% parallel efficiency on 128 GPUs on the Perlmutter supercomputer for real-world datasets.