MGARD+: Optimizing Multilevel Methods for Error-Bounded Scientific Data Reduction

Nowadays, data reduction is becoming increasingly important in dealing with the large amounts of scientific data. Existing multilevel compression algorithms offer a promising way to manage scientific data at scale but may suffer from relatively low performance and reduction quality. In this paper, we propose MGARD+, a multilevel data reduction and refactoring framework drawing on previous multilevel methods, to achieve high-performance data decomposition and high-quality error-bounded lossy compression. Our contributions are four-fold: 1) We propose to leverage a level-wise coefficient quantization method, which uses different error tolerances to quantize the multilevel coefficients. 2) We propose an adaptive decomposition method which treats the multilevel decomposition as a preconditioner and terminates the decomposition process at an appropriate level. 3) We leverage a set of algorithmic optimization strategies to significantly improve the performance of multilevel decomposition/recompositing. 4) We evaluate our proposed method using four real-world scientific datasets and compare with several state-of-the-art lossy compressors. Experiments demonstrate that our optimizations improve the decomposition/recompositing performance of the existing multilevel method by up to $70 \times$70x, and the proposed compression method can improve compression ratio by up to $2 \times$2x compared with other state-of-the-art error-bounded lossy compressors under the same level of data distortion.