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.

翻译：本研究探索了一种在现有误差有界有损压缩器中保持拓扑分割的新范式。当今的有损压缩器很少考虑保持诸如Morse-Smale复形等拓扑结构，原始数据与解压后数据集之间的拓扑差异可能导致错误的解释，甚至得出不正确的科学结论。本文聚焦于在二维/三维分段线性标量场中保持Morse-Smale分割，旨在精确重建由每个顶点的积分线所诱导的极小值/极大值标签。其关键在于在压缩时推导出一系列编辑操作；这些编辑操作应用于解压后的数据，从而在将误差保持在规定误差范围内的同时，实现分割的精确重建。为此，我们开发了一个工作流程，交替修正极值点和积分线直至在有限迭代内收敛；我们通过共享内存/GPU并行化加速每个工作流程组件，使其性能足以与压缩器实际耦合。我们通过流体动力学、海洋学和宇宙学应用数据集展示了使用案例，并在NVIDIA A100 GPU上实现了显著加速。