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Toward fault-tolerant parallel-in-time integration with PFASST

PARALLEL COMPUTING 2017年 62卷 20-37页

作者： Speck, Robert Ruprecht, Daniel Forschungszentrum Julich Julich Supercomp Ctr D-52425 Julich Germany Univ Leeds Sch Mech Engn Woodhouse Lane Leeds LS2 9JT W Yorkshire England

We introduce and analyze different strategies for the parallel-in-time integration method PFASST to recover from hard faults and subsequent data loss. Since PFASST stores solutions at multiple time steps on different processors, information from adjacent steps can be used to recover after a processor has failed. PFASST's multi-level hierarchy allows to use the coarse level for correcting the reconstructed solution, which can help to minimize overhead. A theoretical model is devised linking overhead to the number of additional PFASST iterations required for convergence after a fault. The potential efficiency of different strategies is assessed in terms of required additional iterations for examples of diffusive and advective type. (C) 2016 Elsevier B.V. All rights reserved.

关键词： algorithm-based fault tolerance Resilience Parallel-in-time integration Gray-Scott model Boussinesq equations

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Correcting Soft Errors Online in Fast Fourier Transform 17

Correcting Soft Errors Online in Fast Fourier Transform

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International Conference for High Performance Computing, Networking, Storage and Analysis (SC)

作者： Liang, Xin Chen, Jieyang Tao, Dingwen Li, Sihuan Wu, Panruo Li, Hongbo Ouyang, Kaiming Liu, Yuanlai Song, Fengguang Chen, Zizhong Univ Calif Riverside Riverside CA 92521 USA Indiana Univ Purdue Univ Indianapolis IN 46202 USA

ISBN: (数字)9781450351140

ISBN: (纸本)9781450351140

While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library- one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes;(2) it detects errors in a much more timely manner;and (3) it also has higher numerical stability and better fault coverage.

关键词： algorithm-based fault tolerance Soft Errors DFT FFT FFTW

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Exploiting data representation for fault tolerance

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JOURNAL OF COMPUTATIONAL SCIENCE 2016年 14卷 51-60页

作者： Elliott, J. Hoemmen, M. Mueller, F. North Carolina State Univ Dept Comp Sci Raleigh NC 27695 USA Sandia Natl Labs Ctr Res Comp POB 5800 Albuquerque NM 87185 USA

Incorrect computer hardware behavior may corrupt intermediate computations in numerical algorithms, possibly resulting in incorrect answers. Prior work models misbehaving hardware by randomly flipping bits in memory. We start by accepting this premise, and present an analytic model for the error introduced by a bit flip in an IEEE 754 floating-point number. We then relate this finding to the linear algebra concepts of normalization and matrix equilibration. In particular, we present a case study illustrating that normalizing both vector inputs of a dot product minimizes the probability of a single bit flip causing a large error in the dot product's result. Furthermore, the absolute error is either less than one or very large, which allows detection of large errors. Then, we apply this to the GMRES iterative solver. We count all possible errors that can be introduced through faults in arithmetic in the computationally intensive orthogonalization phase of GMRES, and show that when the matrix is equilibrated, the absolute error is bounded above by one. (C) 2016 Elsevier B.V. All rights reserved.

关键词： algorithm-based fault tolerance Resilient algorithms Numerical methods

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A backward/forward recovery approach for the preconditioned conjugate gradient method

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JOURNAL OF COMPUTATIONAL SCIENCE 2016年第Part3期17卷 522-534页

作者： Fasi, Massimiliano Langou, Julien Robert, Yves Ucar, Bora Univ Manchester Manchester M13 9PL Lancs England Univ Colorado Denver Denver CO USA ENS Lyon Lyon France Univ Tennessee Knoxville TN USA Univ Lyon INRIA CNRS LIPUMR5668ENS LyonUCBL Lyon France

Several recent papers have introduced a periodic verification mechanism to detect silent errors in iterative solvers. Chen (2013, pp. 167-176) has shown how to combine such a verification mechanism (a stability test checking the orthogonality of two vectors and recomputing the residual) with checkpointing: the idea is to verify every d iterations, and to checkpoint every c x d iterations. When a silent error is detected by the verification mechanism, one can rollback to and re-execute from the last checkpoint. In this paper, we also propose to combine checkpointing and verification, but we use algorithm-based fault tolerance (ABFT) rather than stability tests. ABFT can be used for error detection, but also for error detection and correction, allowing a forward recovery (and no rollback nor re-execution) when a single error is detected. We introduce an abstract performance model to compute the performance of all schemes, and we instantiate it using the preconditioned conjugate gradient algorithm. Finally, we validate our new approach through a set of simulations. (C) 2016 Elsevier B.V. All rights reserved.

关键词： fault-tolerance Silent errors algorithm-based fault tolerance Checkpointing Sparse matrix-vector multiplication Preconditioned conjugate gradient method

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Design and analysis of two highly scalable sparse grid combination algorithms

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JOURNAL OF COMPUTATIONAL SCIENCE 2016年第Part3期17卷 547-561页

作者： Strazdins, Peter E. Ali, Md. Mohsin Harding, Brendan Australian Natl Univ Res Sch Comp Sci Canberra ACT 0200 Australia Australian Natl Univ Inst Math Sci Canberra ACT 0200 Australia

Many large scale scientific simulations involve the time evolution of systems modelled as Partial Differential Equations (PDEs). The sparse grid combination technique (SGCT) is a cost-effective method for solve time-evolving PDEs, especially for higher-dimensional problems. It consists of evolving PDE over a set of grids of differing resolution in each dimension, and then combining the results to approximate the solution of the PDE on a grid of high resolution in all dimensions. It can also be extended to support algorithmic-based fault-tolerance, which is also important for computations at this scale. In this paper, we present two new parallel algorithms for the SGCT that supports the full distributed memory parallelization over the dimensions of the component grids, as well as across the grids as well. The direct algorithm is so called because it directly implements a SGCT combination formula. We give details of the design and implementation of a 'partial' sparse grid data structure, which is needed for its efficient implementation. The second algorithm converts each component grid into their hierarchical surpluses, and then uses the direct algorithm on each of the hierarchical surpluses. The conversion to/from the hierarchical surpluses is also an important algorithm in its own right. It requires a technique called sub-griding in order to correctly deal with the combination of very small surpluses. An analysis of both indicates the direct algorithm minimizes the number of messages, whereas the hierarchical surplus minimizes memory consumption and offers a reduction in bandwidth by a factor of 1-2(-d), where d is the dimensionality of the SGCT. However, this is offset by its incomplete parallelism (70-80%) and a factor of 2(d) load imbalance in practical scenarios. Our analysis also indicates both are suitable in a bandwidth limited regime and that the direct algorithm is scalable with respect to d. Experimental results including the strong and weak scalability of

关键词： High performance computing Parallel computing PDE solvers Sparse grid combination technique algorithm-based fault tolerance

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Reliable Linear, Sesquilinear, and Bijective Operations on Integer Data Streams Via Numerical Entanglement

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第17期64卷 4606-4617页

作者： Anam, Mohammad Ashraful Andreopoulos, Yiannis UCL Elect & Elect Engn Dept London WC1E 7JE England

A new technique is proposed for fault-tolerant linear, sesquilinear and bijective (LSB) operations onM integer data streams (M >= 3), such as: scaling, additions/subtractions, inner or outer vector products, permutations and convolutions. In the proposed method, M input integer data streams are linearly superimposed to form M numerically-entangled integer data streams that are stored in-place of the original inputs. LSB operations can then be performed directly using these entangled data streams. The results are extracted from the M entangled output streams by additions and arithmetic shifts. Any soft errors affecting one disentangled output stream are guaranteed to be detectable via a post-computation reliability check. Additionally, when utilizing a separate processor core for each stream, our approach can recover all outputs after any single fail-stop failure. Importantly, unlike algorithm-based fault tolerance (ABFT) methods, the number of operations required for the entire process is linearly related to the number of inputs and does not depend on the complexity of the performed LSB operations. We have validated our proposal in an Intel processor via several types of operations: fast Fourier transforms, convolutions, and matrix multiplication operations. Our analysis and experiments reveal that the proposed approach incurs between 0.03% to 7% reduction in processing throughput for numerous LSB operations. This overhead is 5 to 1000 times smaller than that of the equivalent ABFT method that uses a checksum stream. Thus, our proposal can be used in fault-generating processor hardware or safety-critical applications, where high reliability is required without the cost of ABFT or modular redundancy.

关键词： Linear operations sum-of-products algorithm-based fault tolerance silent data corruption core failures numerical entanglement

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In-Situ Mitigation of Silent Data Corruption in PDE Solvers

In-Situ Mitigation of Silent Data Corruption in PDE Solvers

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ACM Workshop on fault-tolerance for HPC at Extreme Scale (FTXS)

作者： Salloum, Maher Mayo, Jackson R. Armstrong, Robert C. Sandia Natl Labs Livermore CA 94551 USA

ISBN: (纸本)9781450343497

We present algorithmic techniques for parallel PDE solvers that leverage numerical smoothness properties of physics simulation to detect and correct silent data corruption within local computations. We initially model such silent hardware errors (which are of concern for extreme scale) via injected DRAM bit flips. Our mitigation approach generalizes previously developed "robust stencils" and uses modified linear algebra operations that spatially interpolate to replace large outlier values. Prototype implementations for 1D hyperbolic and 3D elliptic solvers, tested on up to 2048 cores, show that this error mitigation enables tolerating orders of magnitude higher bit-flip rates. The runtime overhead of the approach generally decreases with greater solver scale and complexity, becoming no more than a few percent in some cases. A key advantage is that silent data corruption can be handled transparently with data in cache, reducing the cost of false-positive detections compared to rollback approaches.

关键词： Silent data corruption resilience algorithm-based fault tolerance partial differential equation numerical methods

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Quality Aware Error Detection in 2-D Separable Linear Transformation 25

Quality Aware Error Detection in 2-D Separable Linear Transf...

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25th IEEE Asian Test Symposium (ATS)

作者： Hu, Shih-Hsin Abraham, Jacob A. Univ Texas Austin Comp Engn Res Ctr Austin TX 78712 USA Qualcomm Technol Inc San Diego CA 92121 USA

ISBN: (纸本)9781509038091

In this paper, we propose a generic weighted check-sum code based quality aware error detection scheme for 2D separable linear transformation. These key components are widely used in multimedia compression systems, e.g., video and image codecs. The technique encodes the input array at the 2D linear transformation level, and algorithms are designed to operate on encoded data and produce encoded output data. The proposed error detection technique is a system-level method therefore can be used in existing hardware or software 2-D linear transformation architectures with low overhead. More importantly, the proposed weighted checksum code based error detection can enable quality metric aware error detection which only flags an error when the quality of the result is lower than expectation. The error tolerance detection technique can fit perfectly in multimedia compression systems.

关键词： algorithm-based fault tolerance linear transform discrete cosine transform discrete wavelet transform

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Application fault tolerance for Shrinking Resources via the Sparse Grid Combination Technique 30

Application Fault Tolerance for Shrinking Resources via the ...

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30th IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Strazdins, Peter E. Ali, Md Mohsin Debusschere, Bert Australian Natl Univ Res Sch Comp Sci Canberra ACT 0200 Australia Sandia Natl Labs Combust Res Facil Livermore CA USA

ISBN: (纸本)9781509036820

The need to make large-scale scientific simulations resilient to the shrinking and growing of compute resources arises from exascale computing and adverse operating conditions (fault tolerance). It can also arise from the cloud computing context where the cost of these resources can fluctuate. In this paper, we describe how the Sparse Grid Combination Technique can make such applications resilient to shrinking compute resources. The solution of the non-trivial issues of dealing with data redistribution and on-the-fly malleability of process grid information and ULFM MPI communicators are described. Results on a 2D advection solver indicate that process recovery time is significantly reduced from the alternate strategy where failed resources are replaced, overall execution time is actually improved from this case and for checkpointing and the execution error remains small, even when multiple failures occur.

关键词： algorithm-based fault tolerance ULFM process failure recovery PDE solvers sparse grid combination technique parallel computing elasticity cloud computing

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fault TOLERANT COMPUTATION WITH THE SPARSE GRID COMBINATION TECHNIQUE

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2015年第3期37卷 C331-C353页

作者： Harding, Brendan Hegland, Markus Larson, Jay Southern, James Australian Natl Univ Inst Math Sci Acton ACT 2601 Australia Fujitsu Labs Europe Hayes UB4 8FE Middx England

This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J. Electron. Suppl., 54 (2013), pp. C394-C411]. This approach to fault tolerance is novel for two reasons: First, the combination technique adds an additional level of parallelism, and second, it provides algorithm-based fault tolerance so that solutions can still be recovered if failures occur during computation. Previous work indicates how the combination technique may be adapted for a low number of faults. In this paper we develop a generalization of the combination technique for which arbitrary collections of coarse approximations may be combined to obtain an accurate approximation. A general fault tolerant combination technique for large numbers of faults is a natural consequence of this work. Using a renewal model for the time between faults on each node of a high performance computer, we also provide bounds on the expected error for interpolation with this algorithm in the presence of faults. Numerical experiments solving the scalar advection PDE demonstrate that the algorithm is resilient to faults on a real application. It is observed that the time to solution is not significantly affected by the presence of (simulated) faults. Additionally the expected error increases with the number of faults but is relatively small even for high fault rates. A comparison with traditional checkpoint-restart methods applied to the combination technique shows that our approach is highly scalable with respect to the number of faults.

关键词： exascale computing algorithm-based fault tolerance sparse grid combination technique parallel algorithms

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