Data Compression in the Petascale Astronomy Era: a GERLUMPH case study

As the volume of data grows, astronomers are increasingly faced with choices on what data to keep -- and what to throw away. Recent work evaluating the JPEG2000 (ISO/IEC 15444) standards as a future data format standard in astronomy has shown promising results on observational data. However, there is still a need to evaluate its potential on other type of astronomical data, such as from numerical simulations. GERLUMPH (the GPU-Enabled High Resolution cosmological MicroLensing parameter survey) represents an example of a data intensive project in theoretical astrophysics. In the next phase of processing, the ~27 terabyte GERLUMPH dataset is set to grow by a factor of 100 -- well beyond the current storage capabilities of the supercomputing facility on which it resides. In order to minimise bandwidth usage, file transfer time, and storage space, this work evaluates several data compression techniques. Specifically, we investigate off-the-shelf and custom lossless compression algorithms as well as the lossy JPEG2000 compression format. Results of lossless compression algorithms on GERLUMPH data products show small compression ratios (1.35:1 to 4.69:1 of input file size) varying with the nature of the input data. Our results suggest that JPEG2000 could be suitable for other numerical datasets stored as gridded data or volumetric data. When approaching lossy data compression, one should keep in mind the intended purposes of the data to be compressed, and evaluate the effect of the loss on future analysis. In our case study, lossy compression and a high compression ratio do not significantly compromise the intended use of the data for constraining quasar source profiles from cosmological microlensing.Comment: 15 pages, 9 figures, 5 tables. Published in the Special Issue of Astronomy & Computing on The future of astronomical data format

Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

Parallel Implementation of Lossy Data Compression for Temporal Data Sets

Many scientific data sets contain temporal dimensions. These are the data storing information at the same spatial location but different time stamps. Some of the biggest temporal datasets are produced by parallel computing applications such as simulations of climate change and fluid dynamics. Temporal datasets can be very large and cost a huge amount of time to transfer among storage locations. Using data compression techniques, files can be transferred faster and save storage space. NUMARCK is a lossy data compression algorithm for temporal data sets that can learn emerging distributions of element-wise change ratios along the temporal dimension and encodes them into an index table to be concisely represented. This paper presents a parallel implementation of NUMARCK. Evaluated with six data sets obtained from climate and astrophysics simulations, parallel NUMARCK achieved scalable speedups of up to 8788 when running 12800 MPI processes on a parallel computer. We also compare the compression ratios against two lossy data compression algorithms, ISABELA and ZFP. The results show that NUMARCK achieved higher compression ratio than ISABELA and ZFP.Comment: 10 pages, HiPC 201

A Universal Parallel Two-Pass MDL Context Tree Compression Algorithm

Computing problems that handle large amounts of data necessitate the use of lossless data compression for efficient storage and transmission. We present a novel lossless universal data compression algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other blocks can accelerate the computation by a factor of $B$, but degrades the compression quality. Instead, our approach is to first estimate the minimum description length (MDL) context tree source underlying the entire input, and then encode each of the $B$ blocks in parallel based on the MDL source. With this two-pass approach, the compression loss incurred by using more parallel units is insignificant. Our algorithm is work-efficient, i.e., its computational complexity is $O(N/B)$. Its redundancy is approximately $B\log(N/B)$ bits above Rissanen's lower bound on universal compression performance, with respect to any context tree source whose maximal depth is at most $\log(N/B)$. We improve the compression by using different quantizers for states of the context tree based on the number of symbols corresponding to those states. Numerical results from a prototype implementation suggest that our algorithm offers a better trade-off between compression and throughput than competing universal data compression algorithms.Comment: Accepted to Journal of Selected Topics in Signal Processing special issue on Signal Processing for Big Data (expected publication date June 2015). 10 pages double column, 6 figures, and 2 tables. arXiv admin note: substantial text overlap with arXiv:1405.6322. Version: Mar 2015: Corrected a typ

Optimizing Lossy Compression Rate-Distortion from Automatic Online Selection between SZ and ZFP

With ever-increasing volumes of scientific data produced by HPC applications, significantly reducing data size is critical because of limited capacity of storage space and potential bottlenecks on I/O or networks in writing/reading or transferring data. SZ and ZFP are the two leading lossy compressors available to compress scientific data sets. However, their performance is not consistent across different data sets and across different fields of some data sets: for some fields SZ provides better compression performance, while other fields are better compressed with ZFP. This situation raises the need for an automatic online (during compression) selection between SZ and ZFP, with a minimal overhead. In this paper, the automatic selection optimizes the rate-distortion, an important statistical quality metric based on the signal-to-noise ratio. To optimize for rate-distortion, we investigate the principles of SZ and ZFP. We then propose an efficient online, low-overhead selection algorithm that predicts the compression quality accurately for two compressors in early processing stages and selects the best-fit compressor for each data field. We implement the selection algorithm into an open-source library, and we evaluate the effectiveness of our proposed solution against plain SZ and ZFP in a parallel environment with 1,024 cores. Evaluation results on three data sets representing about 100 fields show that our selection algorithm improves the compression ratio up to 70% with the same level of data distortion because of very accurate selection (around 99%) of the best-fit compressor, with little overhead (less than 7% in the experiments).Comment: 14 pages, 9 figures, first revisio