Preserving Discrete Morse-Smale Complexes in Error-Bounded Lossy Compression

TL;DR

This paper introduces a topology-preserving lossy compression method for scientific data that guarantees 100% preservation of Morse-Smale complexes, ensuring accurate downstream analysis.

Contribution

It extends previous segmentation-preserving methods to fully preserve Morse-Smale complexes, including all critical points and separatrices, using an iterative editing strategy with GPU acceleration.

Findings

Achieves 100% preservation of Morse-Smale complexes in experiments.

Effectively corrects topological features in decompressed data from standard compressors.

Balances compression efficiency with topological accuracy through flexible options.

Abstract

Scientific applications are generating unprecedented volumes of data that overwhelm storage and transmission systems, posing significant challenges for the design of data management tools and scientific databases. Lossy compression has emerged as a promising strategy to address this problem, but most existing compressors fail to preserve the topology of scientific data, leading to inaccuracies in downstream analyses and potentially erroneous scientific conclusions. In this work, we present a methodology for fully preserving the topology, specifically, Morse-Smale complexes (MSCs), in lossy-compressed 2D and 3D scalar field data from scientific simulations. We generalize the edit-based strategy introduced in MSz (a previous method that preserves only segmentations and cannot preserve saddles or separatrices) by extending the framework to the full MSCs, including all critical points and separatrices. Our approach corrects the MSCs in the decompressed output of any error-bounded lossy compressor (e.g., SZ3 or ZFP), referred to as the base compressor, using an iterative editing strategy that preserves all critical points and their connectivity via separatrices. During compression, we generate a sequence of quantized edits that are applied to the decompressed output, ensuring accurate preservation of topological features while maintaining the error within prescribed bounds. The strategy iteratively fixes critical points and separatrices in alternating steps until convergence is achieved in a finite number of iterations. To meet diverse application needs, our method offers flexible options that balance compression efficiency with feature preservation. To reduce computation time, we leverage GPU parallelism to accelerate each component of the workflow. Experiments on multiple datasets demonstrate that our method achieves 100% preservation of Morse-Smale complexes.