Resilient N-Body Tree Computations with Algorithm-Based Focused Recovery: Model and Performance Analysis

This paper presents a model and performance study for Algorithm-Based Focused Recovery (ABFR) applied to N-body computations, subject to latent errors. We make a detailed comparison with the classical Checkpoint/Restart (CR) approach. While the model applies to general frameworks, the performance study is limited to perfect binary trees, due to the inherent difficulty of the analysis. With ABFR, the crucial parameter is the detection interval, which bounds the error latency. We show that the detection interval has a dramatic impact on the overhead, and that optimally choosing its value leads to significant gains over the CR approach

Coping with Recall and Precision of Soft Error Detectors

Many methods are available to detect silent errors in high-performancecomputing (HPC) applications. Each comes with a given cost, recall (fractionof all errors that are actually detected, i.e., false negatives),and precision (fraction of true errors amongst all detected errors,i.e., false positives).The main contribution of this paperis to characterize the optimal computing pattern for an application:which detector(s) to use, how many detectors of each type touse, together with the length of the work segment that precedes each of them.We first prove that detectors with imperfect precisions offer limited usefulness.Then we focus on detectors with perfect precision, and weconduct a comprehensive complexity analysis of this optimization problem,showing NP-completeness and designing an FPTAS (Fully Polynomial-TimeApproximation Scheme). On the practical side, we provide a greedy algorithm,whose performance is shown to be close to the optimal for a realistic set ofevaluation scenarios. Extensive simulations illustrate the usefulness of detectorswith false negatives, which are available at a lower cost than guaranteed detectors.De nombreuses méthodes sont disponibles pour détecter les erreurs silencieuses dans les applications de Calcul Haute Performance (HPC). Chaque méthode a un coût, un rappel (fraction de toutes les erreurs qui sont effectivement détectées, i.e., faux négatifs), et une précision (fraction des vraies erreurs parmi toutes les erreurs détectées, i.e., faux positifs). La principale contribution de ctravail est de montrer quel(s) détecteur(s) utiliser, et de caractériser le motif de calcul optimale pour une application: combien de détecteurs de chaque type utiliser, ainsi que la longueur du segment de travail qui les précède.Nous prouvons que les détecteurs avec une précision non parfaite sont d'une utilité limitée. Ainsi, nous nous concentrons sur des détecteurs avec une précision parfaite et nous menons une analyse de complexité exhaustive de ce problème d'optimisation, montrant sa NP-complétude et concevant un schéma FPTAS (Fully Polynomial-Time Approximation Scheme). Sur le plan pratique, nous fournissons un algorithme glouton dont la performance est montrée comme étant proche de l'optimal pour un ensemble réaliste de scénarios d'évaluation. De nombreuses simulations démontrent l'utilité de détecteurs avec des résultats faux-négatifs (i.e., des erreurs non détectées), qui sont disponibles à un coût bien moindre que les détecteurs parfaits

Coping with recall and precision of soft error detectors

International audienceMany methods are available to detect silent errors in high-performance computing (HPC) applications. Each method comes with a cost, a recall (fraction of all errors that are actually detected, i.e., false negatives), and a precision (fraction of true errors amongst all detected errors, i.e., false positives). The main contribution of this paper is to characterize the optimal computing pattern for an application: which detector(s) to use, how many detectors of each type to use, together with the length of the work segment that precedes each of them. We first prove that detectors with imperfect precisions offer limited usefulness. Then we focus on detectors with perfect precision , and we conduct a comprehensive complexity analysis of this optimization problem, showing NP-completeness and designing an FPTAS (Fully Polynomial-Time Approximation Scheme). On the practical side, we provide a greedy algorithm, whose performance is shown to be close to the optimal for a realistic set of evaluation scenarios. Extensive simulations illustrate the usefulness of detectors with false negatives, which are available at a lower cost than the guaranteed detectors

From detection to optimization: impact of soft errors on high-performance computing applications

As high-performance computing (HPC) continues to progress, constraints on HPC system design forces the handling of errors to higher levels in the software stack. Of the types of errors facing HPC, soft errors that silently corrupt system or application state are among the most severe. The behavior of HPC applications in the presence of soft errors is critical to gain insight for effective utilization of HPC systems. The need to understand this behavior can be used in developing algorithm-based error detection guided by application characteristics from fault injection and error propagation studies. Furthermore, the realization that applications are tolerant to small errors allows optimizations such as lossy compression on high-cost data transfers. Lossy compression adds small user controllable amounts of error when compressing data, to reduce data size before expensive data transfers saving time. This dissertation investigates and improves the resiliency of HPC applications to soft errors, and explores lossy compression as a new form of optimization for expensive, time-consuming data transfers

Mitigation of failures in high performance computing via runtime techniques

As machines increase in scale, it is predicted that failure rates of supercomputers will correspondingly increase. Even though the mean time to failure (MTTF) of individual component is high, the large number of components significantly decreases the system MTTF. Meanwhile, the decreasing size of transistors has been critical to the increase in capacity of supercomputers. The smaller the transistors are, silent data corruptions (SDC) are likely to occur more frequently. SDCs do not inhibit execution, but may silently lead to incorrect results. In this thesis, we leverage runtime system and compiler techniques to mitigate a significant fraction of failures automatically with low overhead. The main goals of various system-level fault tolerance strategies designed in this thesis are: reducing the extra cost added to application execution while improving system reliability; automatically adjusting fault tolerance decisions without user intervention based on environmental changes; protecting applications not only from fail-stop failures but also from silent data corruptions. The main contributions of this thesis are development of a semi-blocking checkpoint protocol that overlaps application execution with fault tolerance operation to reduce the overhead of checkpointing, a runtime system technique for automatic checkpoint and restart without user intervention, a holistic framework (ACR) for automatically detecting and recovering from silent data corruptions and a framework called FlipBack that provides targeted protection against silent data corruption with low cost

Scaling and Resilience in Numerical Algorithms for Exascale Computing

The first Petascale supercomputer, the IBM Roadrunner, went online in 2008. Ten years later, the community is now looking ahead to a new generation of Exascale machines. During the decade that has passed, several hundred Petascale capable machines have been installed worldwide, yet despite the abundance of machines, applications that scale to their full size remain rare. Large clusters now routinely have 50.000+ cores, some have several million. This extreme level of parallelism, that has allowed a theoretical compute capacity in excess of a million billion operations per second, turns out to be difficult to use in many applications of practical interest. Processors often end up spending more time waiting for synchronization, communication, and other coordinating operations to complete, rather than actually computing. Component reliability is another challenge facing HPC developers. If even a single processor fail, among many thousands, the user is forced to restart traditional applications, wasting valuable compute time. These issues collectively manifest themselves as low parallel efficiency, resulting in waste of energy and computational resources. Future performance improvements are expected to continue to come in large part due to increased parallelism. One may therefore speculate that the difficulties currently faced, when scaling applications to Petascale machines, will progressively worsen, making it difficult for scientists to harness the full potential of Exascale computing. The thesis comprises two parts. Each part consists of several chapters discussing modifications of numerical algorithms to make them better suited for future Exascale machines. In the first part, the use of Parareal for Parallel-in-Time integration techniques for scalable numerical solution of partial differential equations is considered. We propose a new adaptive scheduler that optimize the parallel efficiency by minimizing the time-subdomain length without making communication of time-subdomains too costly. In conjunction with an appropriate preconditioner, we demonstrate that it is possible to obtain time-parallel speedup on the nonlinear shallow water equation, beyond what is possible using conventional spatial domain-decomposition techniques alone. The part is concluded with the proposal of a new method for constructing Parallel-in-Time integration schemes better suited for convection dominated problems. In the second part, new ways of mitigating the impact of hardware failures are developed and presented. The topic is introduced with the creation of a new fault-tolerant variant of Parareal. In the chapter that follows, a C++ Library for multi-level checkpointing is presented. The library uses lightweight in-memory checkpoints, protected trough the use of erasure codes, to mitigate the impact of failures by decreasing the overhead of checkpointing and minimizing the compute work lost. Erasure codes have the unfortunate property that if more data blocks are lost than parity codes created, the data is effectively considered unrecoverable. The final chapter contains a preliminary study on partial information recovery for incomplete checksums. Under the assumption that some meta knowledge exists on the structure of the data encoded, we show that the data lost may be recovered, at least partially. This result is of interest not only in HPC but also in data centers where erasure codes are widely used to protect data efficiently

Toward Resilience and Data Reduction in Exascale Scientific Computing

Because of the ever-increasing execution scale, reliability and data management are becoming more and more important for scientific applications. On the one hand, exascale systems are anticipated to be more susceptible to soft errors ,e.g. silent data corruptions, due to the reduction in the size of transistors and the increase of the number of components. These errors will lead to corrupted results without warning, making the output of the computation untrustable. On the other hand, large volumes of highly variable data are produced by scientific computing with high velocity on exascale systems or advanced instruments, and the I/O time on storing these data is prohibitive due to the I/O bottleneck in parallel file systems. In this work, we leverage algorithm-based fault tolerance (ABFT) and error-bound lossy compression to tackle the two problems, in order to support efficient scientific computing on exascale systems.We propose an efficient fault tolerant scheme to tolerant soft errors in Fast Fourier Transform (FFT), one of the most important computation kernels widely used in scientific computing. Traditional redundancy approaches will at least double the execution time or resources, limiting the usage in practice because of the large overhead. Previous works on offline ABFT algorithms for FFT mitigate this problem by providing resilient FFT with lower overhead, but these algorithms fail to make progress in vulnerable environments with high error rates because they can only detect and correct errors after the whole computation finishes. We propose an online ABFT scheme for large-scale FFT inspired by the divide-and-conquer nature of the FFT computation. We devise fault tolerant schemes for both computational and memory errors in FFT, with both serial and parallel optimizations. Experimental results demonstrate that the proposed approach provides more timely error detection and recovery as well as better fault coverage with less overhead, compared to the offline ABFT algorithm.To alleviate the I/O bottleneck in the parallel file systems, we work on a prediction-based error-bounded lossy compressor to significantly reduce the size of scientific datasets while retaining the accuracy of the decompressed data, with adaptive prediction algorithms and compression models. We first propose a regression-based predictor for better prediction accuracy than traditional approaches under large error bounds, followed by an adaptive algorithm that dynamically selects between the traditional Lorenzo predictor and the proposed regression-based predictor, leading to very high compression ratios with little visual distortion. We further unify the prediction-based model and transform-baed model by using transform-based compressors as a predictor, with novel optimizations toward efficient coefficient encoding for both the two models. The proposed adaptive multi-algorithm design provides better compression ratios given the same distortion, significantly reducing storage requirements and I/O time.We further adapt the compression algorithms and compressors to different requirements and/or objectives in realistic scenarios. We leverage a logarithmic transform to precondition the data, which turns a relative-error-bound compression problem into an absolute-error-bound compression problem. This transform aligns two different error requirements while improving the compression quality, efficiently reducing the workload for compressor design. We also correlate the compression algorithm with system information to achieve better I/O performance compared to traditional single compressor deployment. These studies further improve the efficiency of lossy compression from the perspective of efficient I/O in the context of scientific simulation, making scientific applications running on exascale systems more efficient

A checkpointing mechanism for GPU intensive HPC applications

Please refer to pdf.James Watt ScholarshipEngineering and Physical Sciences Research Council (EPSRC) grants EP/N028201/1 and EP/L00058X/