What Polynomial Regression Reveals About Scientific Data Compression

Scientific instruments and large-scale simulations produce vast amounts of floating-point data, posing challenges for storage, transfer, and analysis. Modern lossy compression reduces data size within error limits but often obscures local data behavior. Consequently, compression is seen mainly as a tool for size reduction rather than a means of learning about the data. Polynomial regression offers another option. Fitting simple mathematical curves to small regions of data can both reduce data size and highlight features such as smooth trends, abrupt changes, and noisy regions. In this work, we examine piecewise polynomial regression as a structure-aware form of compression. Our goal is less about outperforming other compressors and more about showing how locally fitted models can expose the underlying structure of the data.