Time-varying Vector Field Compression with Preserved Critical Point Trajectories

2025-10-28

AI Summary

Time-varying vector field data are large-scale, and existing lossy compression methods fail to faithfully reconstruct critical point trajectories—hindering scientific analysis. To address this, we propose the first efficient lossy compression framework that *provably guarantees exact reconstruction of all critical point trajectories*. Our method extends spatial critical point preservation theory to the spatiotemporal domain for trajectory-level geometric fidelity; introduces a hybrid semi-Lagrangian–Lorenzo predictor that jointly models spatiotemporal correlations; and integrates an error-bounded encoding strategy. Evaluated on real scientific datasets, our framework achieves a peak compression ratio of 124.48×—56.07× higher than the best lossless alternative—while uniquely preserving *all* critical point trajectories at this ratio. This represents the first lossy compression approach with theoretical trajectory reconstruction guarantees for time-varying vector fields.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Scientific simulations and observations are producing vast amounts of time-varying vector field data, making it hard to store them for archival purposes and transmit them for analysis. Lossy compression is considered a promising approach to reducing these data because lossless compression yields low compression ratios that barely mitigate the problem. However, directly applying existing lossy compression methods to timevarying vector fields may introduce undesired distortions in critical-point trajectories, a crucial feature that encodes key properties of the vector field. In this work, we propose 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 for preserving critical points in space to preserving critical-point trajectories in space-time, and develop a compression framework to realize the functionality. Second, we propose a semi-Lagrange predictor to exploit the spatiotemporal correlations in advectiondominated regions, and combine it with the traditional Lorenzo predictor for improved compression efficiency. Third, we evaluate our method against state-of-the-art lossy and lossless compressors using four real-world scientific datasets. Experimental results demonstrate that the proposed method delivers up to 124.48X compression ratios while effectively preserving all critical-point trajectories. This compression ratio is up to 56.07X higher than that of the best lossless compressors, and none of the existing lossy compressors can preserve all critical-point trajectories at similar compression ratios.

Problem

• Compressing large time-varying vector field data efficiently
• Preserving critical-point trajectories during lossy compression
• Improving compression ratios while maintaining essential field features

Innovation

• Preserves all critical-point trajectories exactly
• Uses semi-Lagrange and Lorenzo predictors
• Achieves high compression ratios effectively