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 variablelength 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 bitrates) 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 bitrates.

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As the number of processors in today's high performance computers continues to grow, the mean-time-to-failure of these computers are becoming significantly shorter than the execution time of many current high performance computing applications. Although today's architectures are usually robust enough to survive node failures without suffering complete system failure, most today's high performance computing applications can not survive node failures and, therefore, whenever a node fails, have to abort themselves and restart from the beginning or a stable-storage-based checkpoint.This paper explores the use of the floating-point arithmetic coding approach to build fault survivable high performance computing applications so that they can adapt to node failures without aborting themselves. Despite the use of erasure codes over Galois field has been theoretically attempted before in diskless checkpointing, few actual implementations exist. This probably derives from concerns related to both the efficiency and the complexity of implementing such codes in high performance computing applications. In this paper, we introduce the simple but efficient floating-point arithmetic coding approach into diskless checkpointing and address the associated round-off error issue. We also implement a floating-point arithmetic version of the Reed-Solomon coding scheme into a conjugate gradient equation solver and evaluate both the performance and the numerical impact of this scheme. Experimental results demonstrate that the proposed floating-point arithmetic coding approach is able to survive a small number of simultaneous node failures with low performance overhead and little numerical impact. *

Several recovery techniques for parallel iterative methods are presented. First, the implementation of checkpoints in parallel iterative methods is described and analyzed. Then a simple checkpoint-free fault-tolerant scheme for parallel iterative methods, the lossy approach, is presented. When one processor fails and all its data is lost, the system is recovered by computing a new approximate solution using the data of the nonfailed processors. The iterative method is then restarted with this new vector. The main advantage of the lossy approach over standard checkpoint algorithms is that it does not increase the computational cost of the iterative solver when no failure occurs. Experiments are presented that compare the different techniques. The fault-tolerant FT-MPI library is used. Both iterative linear solvers and eigensolvers are considered.

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