Time-varying Vector Field Compression with Preserved Critical Point Trajectories

TL;DR

This work tackles the challenge of compressing time-varying vector fields while exactly preserving all critical-point trajectories. It advances the theory from preserving critical points in space to preserving trajectories in space-time by space-time extrusion and a robust face-level test guided by Simulation of Simplicity. A block-wise Mixture of Predictors (MoP), combining a Semi-Lagrangian predictor with a traditional 3D-Lorenzo predictor, achieves high compression ratios while enforcing a bound $\|\ abla - \nabla\|$ on the original data and invariant face predicates that guarantee trajectory preservation. Evaluations on four real-world datasets show up to $124.48\times$ compression and up to $56.07\times$ gains over lossless compressors, with existing lossy methods failing to preserve CP trajectories at comparable rates. The approach enables efficient, topology-aware storage and analysis of CP trajectories in large-scale simulations and observations, and is amenable to streaming, parallelization, and potential GPU acceleration.

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.

Figures (12)

• Figure 1: (a) presents an example of the temporal evolution of the critical point and the corresponding events; (b) illustrates how lossy compression alters the critical point, leading to a change in its trajectory.
• Figure 2: Space-Time extrusion of simplicial mesh. (a) A 2D triangle is extruded along the temporal dimension to form a prism. (b) A triangular prism is structurally subdivided into three tetrahedra. (c) A 2D simplicial mesh is extruded into a 3D prismatic mesh and subsequently subdivided.
• Figure 3: Overview of the proposed framework.
• Figure 4: RK2 and adaptive substepping method in semi-Lagrangian predictor. The green dashed arrows indicate the departure point traceback (Eq. \ref{['eq:sl-dep']}), while the light blue dashed arrows represent the bilinear interpolation (Eq. \ref{['eq:sl-sample']}).
• Figure 5: Rate-distortion under different datasets.

Theorems & Definitions (5)

• Lemma 1: Zero-set in a tetrahedron
• Theorem 1: Per-time critical point preservation
• proof : Sketch
• Theorem 2: Track equivalence
• proof : Sketch