Fast Topology-Aware Lossy Data Compression with Full Preservation of Critical Points and Local Order

2026-03-27

AI Summary

Scientific computing and instrument-generated floating-point data demand efficient compression, yet existing lossy methods struggle to rigorously preserve topological structures—such as critical points and local ordering—under high compression ratios. This work proposes a novel lossy compressor that, for the first time, achieves high-speed, high-ratio compression while strictly preserving all critical points and the complete local ordering of values. The method substantially outperforms current topology-preserving compression techniques: it accelerates compression by multiple orders of magnitude, surpasses lossless schemes in compression ratio, and guarantees bit-wise identical outputs across CPU and GPU executions.

Abstract

Many scientific codes and instruments generate large amounts of floating-point data at high rates that must be compressed before they can be stored. Typically, only lossy compression algorithms deliver high-enough compression ratios. However, many of them provide only point-wise error bounds and do not preserve topological aspects of the data such as the relative magnitude of neighboring points. Even topology-preserving compressors tend to merely preserve some critical points and are generally slow. Our Local-Order-Preserving Compressor is the first to preserve the full local order (and thus all critical points), runs orders of magnitude faster than prior topology-preserving compressors, yields higher compression ratios than lossless compressors, and produces bit-for-bit the same output on CPUs and GPUs.

Problem

• lossy compression
• topology preservation
• critical points
• local order
• scientific data

Innovation

• topology-aware compression
• local order preservation
• critical points
• lossy data compression
• cross-platform reproducibility