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

Area of Science:

• Data Science
• Scientific Computing
• Topology

Background:

• Scientific data volumes are rapidly increasing, straining storage and transmission.
• Existing lossy compression methods often fail to preserve critical topological features, compromising data analysis accuracy.

Purpose of the Study:

• To develop a methodology for fully preserving Morse-Smale complexes (MSCs) in lossy-compressed scientific data.
• To extend previous edit-based strategies to encompass all topological features, including critical points and separatrices.

Main Methods:

• An iterative editing strategy is employed to correct decompressed data, preserving all critical points and their connectivity.
• Quantized edits are generated during compression to ensure topological accuracy within error bounds.
• GPU parallelism is utilized to accelerate the computational workflow.

Main Results:

• The proposed method achieves 100% preservation of Morse-Smale complexes in 2D and 3D scalar field data.
• The approach is compatible with existing error-bounded lossy compressors like SZ3 and ZFP.
• Flexible options are available to balance compression efficiency with feature preservation.

Conclusions:

• This methodology enables accurate topological analysis of lossy-compressed scientific data.
• It addresses a critical limitation in current data compression techniques for scientific applications.
• The method offers a robust solution for managing large-scale scientific datasets without sacrificing topological integrity.