Scientific data often exhibits well-defined model mechanisms, which can be characterized by differential equations. However, existing compression algorithms face challenges in distinguishing between information that encapsulates underlying mechanisms and redundant information in the data. Accordingly, these algorithms struggle to accurately assess the true level of meaningful precision [1] . To address this issue, we propose a compression method that incorporates mechanism learning and effective precision identification. By locally characterizing the data’s spatial relationship with linear differential equations and minimizing the source term, we learn the mechanisms. This allows us to separate noise from the data while preserving its precision. Thus, detectable patterns are more likely to emerge, enabling effective compression [2] .

Lossless compression of large-scale scientific floating-point data is critical yet challenging due to the presence of high-order information and noise that arises from model truncation and discretization errors. Existing entropy coding techniques fail to effectively leverage the mechanisms underlying the data generation process. This paper introduces MeLLoC(Mechanism Learning for Lossless Compression), a novel approach that combines high-order mechanism learning with classical encoding to enhance lossless compression for scientific data. The key idea is to treat the data as discrete samples from an underlying physical field described by differential equations and solve an inverse problem to identify the governing equation coefficients exhibiting more compressible numeric representations. Periodic extension techniques are employed to accelerate the decompression. Through extensive experiments on various scientific datasets, MeLLoC consistently outperforms state-of-the-art lossless compressors while offering compelling trade-offs between compression ratios and computational costs. This work opens up new avenues for exploiting domain knowledge and high-order information to improve data compression in scientific computing.