MSz: An Efficient Parallel Algorithm for Correcting Morse-Smale Segmentations in Error-Bounded Lossy Compressors

TL;DR

This paper introduces MSz, a parallel algorithm that preserves Morse-Smale topological segmentations in lossy data compression, ensuring accurate scientific analysis while maintaining error bounds.

Contribution

It presents a novel parallel workflow for correcting Morse-Smale segmentations during compression, accelerating the process with GPU parallelism for practical use.

Findings

Achieves accurate segmentation reconstruction within error bounds.

Significantly accelerates the process using GPU parallelism.

Demonstrates effectiveness on fluid dynamics, ocean, and cosmology datasets.

Abstract

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.