arXiv subjects

Zizhong Chen

Publications and source records attributed to Zizhong Chen.

43 records · Page 3Linked to original sources

arXiv2018

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.

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arXiv2017

In-Depth Exploration of Single-Snapshot Lossy Compression Techniques for N-Body Simulations

In situ lossy compression allowing user-controlled data loss can significantly reduce the I/O burden. For large-scale N-body simulations where only one snapshot can be compressed at a time, the lossy compression ratio is very limited because of the fairly low spatial coherence of the particle data. In this work, we assess the state-of-the-art single-snapshot lossy compression techniques of two common N-body simulation models: cosmology and molecular dynamics. We design a series of novel optimization techniques based on the two representative real-world N-body simulation codes. For molecular dynamics simulation, we propose three compression modes (i.e., best speed, best tradeoff, best compression mode) that can refine the tradeoff between the compression rate (a.k.a., speed/throughput) and ratio. For cosmology simulation, we identify that our improved SZ is the best lossy compressor with respect to both compression ratio and rate. Its compression ratio is higher than the second-best compressor by 11% with comparable compression rate. Experiments with up to 1024 cores on the Blues supercomputer at Argonne show that our proposed lossy compression method can reduce I/O time by 80% compared with writing data directly to a parallel file system and outperforms the second-best solution by 60%. Moreover, our proposed lossy compression methods have the best rate-distortion with reasonable compression errors on the tested N-body simulation data compared with state-of-the-art compressors.

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arXiv2017

Z-checker: A Framework for Assessing Lossy Compression of Scientific Data

Because of vast volume of data being produced by today's scientific simulations and experiments, lossy data compressor allowing user-controlled loss of accuracy during the compression is a relevant solution for significantly reducing the data size. However, lossy compressor developers and users are missing a tool to explore the features of scientific datasets and understand the data alteration after compression in a systematic and reliable way. To address this gap, we have designed and implemented a generic framework called Z-checker. On the one hand, Z-checker combines a battery of data analysis components for data compression. On the other hand, Z-checker is implemented as an open-source community tool to which users and developers can contribute and add new analysis components based on their additional analysis demands. In this paper, we present a survey of existing lossy compressors. Then we describe the design framework of Z-checker, in which we integrated evaluation metrics proposed in prior work as well as other analysis tools. Specifically, for lossy compressor developers, Z-checker can be used to characterize critical properties of any dataset to improve compression strategies. For lossy compression users, Z-checker can detect the compression quality, provide various global distortion analysis comparing the original data with the decompressed data and statistical analysis of the compression error. Z-checker can perform the analysis with either coarse granularity or fine granularity, such that the users and developers can select the best-fit, adaptive compressors for different parts of the dataset. Z-checker features a visualization interface displaying all analysis results in addition to some basic views of the datasets such as time series. To the best of our knowledge, Z-checker is the first tool designed to assess lossy compression comprehensively for scientific datasets.

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arXiv2017

Exploration of Pattern-Matching Techniques for Lossy Compression on Cosmology Simulation Data Sets

Because of the vast volume of data being produced by today's scientific simulations, lossy compression allowing user-controlled information loss can significantly reduce the data size and the I/O burden. However, for large-scale cosmology simulation, such as the Hardware/Hybrid Accelerated Cosmology Code (HACC), where memory overhead constraints restrict compression to only one snapshot at a time, the lossy compression ratio is extremely limited because of the fairly low spatial coherence and high irregularity of the data. In this work, we propose a pattern-matching (similarity searching) technique to optimize the prediction accuracy and compression ratio of SZ lossy compressor on the HACC data sets. We evaluate our proposed method with different configurations and compare it with state-of-the-art lossy compressors. Experiments show that our proposed optimization approach can improve the prediction accuracy and reduce the compressed size of quantization codes compared with SZ. We present several lessons useful for future research involving pattern-matching techniques for lossy compression.

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arXiv2017

Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error-Controlled Quantization

Today's HPC applications are producing extremely large amounts of data, such that data storage and analysis are becoming more challenging for scientific research. In this work, we design a new error-controlled lossy compression algorithm for large-scale scientific data. Our key contribution is significantly improving the prediction hitting rate (or prediction accuracy) for each data point based on its nearby data values along multiple dimensions. We derive a series of multilayer prediction formulas and their unified formula in the context of data compression. One serious challenge is that the data prediction has to be performed based on the preceding decompressed values during the compression in order to guarantee the error bounds, which may degrade the prediction accuracy in turn. We explore the best layer for the prediction by considering the impact of compression errors on the prediction accuracy. Moreover, we propose an adaptive error-controlled quantization encoder, which can further improve the prediction hitting rate considerably. The data size can be reduced significantly after performing the variable-length encoding because of the uneven distribution produced by our quantization encoder. We evaluate the new compressor on production scientific data sets and compare it with many other state-of-the-art compressors: GZIP, FPZIP, ZFP, SZ-1.1, and ISABELA. Experiments show that our compressor is the best in class, especially with regard to compression factors (or bit-rates) and compression errors (including RMSE, NRMSE, and PSNR). Our solution is better than the second-best solution by more than a 2x increase in the compression factor and 3.8x reduction in the normalized root mean squared error on average, with reasonable error bounds and user-desired bit-rates.

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arXiv2015

Algorithmic Energy Saving for Parallel Cholesky, LU, and QR Factorizations

The pressing demands of improving energy efficiency for high performance scientific computing have motivated a large body of software-controlled hard- ware solutions using Dynamic Voltage and Frequency Scaling (DVFS) that strategically switch processors to low-power states, when the peak processor performance is not necessary. Although OS level solutions have demonstrated the effectiveness of saving energy in a black-box fashion, for applications with variable execution characteristics, the optimal energy efficiency can be blundered away due to defective prediction mechanism and untapped load imbalance. In this paper, we propose TX, a library level race-to-halt DVFS scheduling approach that analyzes Task Dependency Set of each task in parallel Cholesky, LU, and QR factorizations to achieve substantial energy savings OS level solutions cannot fulfill. Partially giving up the generality of OS level solutions per requiring library level source modification, TX lever- ages algorithmic characteristics of the applications to gain greater energy savings. Experimental results on two power-aware clusters indicate that TX can save up to 17.8% more energy than state-of-the-art OS level solutions with negligible 3.5% on average performance loss.

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arXiv2008

Condition Numbers of Gaussian Random Matrices

Let $G_{m \times n}$ be an $m \times n$ real random matrix whose elements are independent and identically distributed standard normal random variables, and let $κ_2(G_{m \times n})$ be the 2-norm condition number of $G_{m \times n}$. We prove that, for any $m \geq 2$, $n \geq 2$ and $x \geq |n-m|+1$, $κ_2(G_{m \times n})$ satisfies $ \frac{1}{\sqrt{2π}} ({c}/{x})^{|n-m|+1} < P(\frac{κ_2(G_{m \times n})} {{n}/{(|n-m|+1)}}> x) < \frac{1}{\sqrt{2π}} ({C}/{x})^{|n-m|+1}, $ where $0.245 \leq c \leq 2.000$ and $ 5.013 \leq C \leq 6.414$ are universal positive constants independent of $m$, $n$ and $x$. Moreover, for any $m \geq 2$ and $n \geq 2$, $ E(\logκ_2(G_{m \times n})) < \log \frac{n}{|n-m|+1} + 2.258. $ A similar pair of results for complex Gaussian random matrices is also established.

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