Bridging Information Theory and Practice for Scientific Lossy Compression

Error-bounded lossy compressors have been developed for years to reduce the vast volumes of scientific data generated by high-performance computing (HPC) applications and advanced scientific instruments. While these compressors have been effective in mitigating the challenges posed by massive datasets, a significant gap remains in our understanding of the fundamental compressibility limits of scientific data–an issue that critically impacts the sustainable adoption and development of efficient lossy compression techniques in practice. Classical rate-distortion theory, established by Shannon, assumes stationary 1D sources with unconstrained coding–assumptions that do not hold for scientific datasets compressed under the tiling constraints imposed by modern parallel lossy compressors. This paper addresses this gap by developing a novel framework that characterizes compressibility limits for scientific datasets under realistic tiling constraints. The contribution is two-fold. First, we establish a tile-aware, finite-blocklength extension of rate–distortion theory that advances classical 1D asymptotic formulations into a rigorous framework for piecewise 2D Gaussian random fields. To our knowledge, this is the first framework to rigorously characterize lossy compressibility limits for scientific datasets and compressor, moving beyond classical asymptotic 1D source models. Second, we conduct a comprehensive validation of the proposed modeling framework using state-of-the-art error-bounded lossy compressors and diverse real-world HPC datasets, demonstrating that our theory accurately predicts rate-distortion trends and provides actionable insights for compressor design.