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

Toward an Optimal Online Checkpoint Solution under a Two-Level HPC Checkpoint Model

The traditional single-level checkpointing method suffers from significantoverhead on large-scale platforms. Hence, multilevel checkpointing protocols have been studied extensively in recent years. The multilevel checkpoint approach allows different levels of checkpoints to be set (each with different checkpoint overheads and recovery abilities), in order to further improve the fault tolerance performance of extreme-scale HPC applications. How to optimize the checkpoint intervals for each level, however, is an extremely difficult problem. In this paper, we construct an easy-to-use two-level checkpoint model. Checkpoint level 1 deals with errors with low checkpoint/recovery overheads such as transient memory errors, while checkpoint level 2 deals with hardware crashes such as node failures.Compared with previous optimization work, our new optimal checkpoint solution offers two improvements: (1) it is an online solution without requiring knowledge of the job length in advance, and (2) it shows that periodic patterns are optimal and determines the best pattern. We evaluate the proposed solution and compare it with the most up-to-date related approaches on an extreme-scale simulation testbed constructed based on a real HPC application execution. Simulation results show that our proposed solution outperforms other optimized solutions and can improve the performance significantly in some cases. Specifically, with the new solution the wall-clock time can be reduced by up to 25.3\% over that of other state-of-the-art approaches. Finally, a brute-force comparison with all possible patterns shows that our solution is always within $1\%$ of the best pattern in the experiments

Resource management for extreme scale high performance computing systems in the presence of failures

2018 Summer.Includes bibliographical references.High performance computing (HPC) systems, such as data centers and supercomputers, coordinate the execution of large-scale computation of applications over tens or hundreds of thousands of multicore processors. Unfortunately, as the size of HPC systems continues to grow towards exascale complexities, these systems experience an exponential growth in the number of failures occurring in the system. These failures reduce performance and increase energy use, reducing the efficiency and effectiveness of emerging extreme-scale HPC systems. Applications executing in parallel on individual multicore processors also suffer from decreased performance and increased energy use as a result of applications being forced to share resources, in particular, the contention from multiple application threads sharing the last-level cache causes performance degradation. These challenges make it increasingly important to characterize and optimize the performance and behavior of applications that execute in these systems. To address these challenges, in this dissertation we propose a framework for intelligently characterizing and managing extreme-scale HPC system resources. We devise various techniques to mitigate the negative effects of failures and resource contention in HPC systems. In particular, we develop new HPC resource management techniques for intelligently utilizing system resources through the (a) optimal scheduling of applications to HPC nodes and (b) the optimal configuration of fault resilience protocols. These resource management techniques employ information obtained from historical analysis as well as theoretical and machine learning methods for predictions. We use these data to characterize system performance, energy use, and application behavior when operating under the uncertainty of performance degradation from both system failures and resource contention. We investigate how to better characterize and model the negative effects from system failures as well as application co-location on large-scale HPC computing systems. Our analysis of application and system behavior also investigates: the interrelated effects of network usage of applications and fault resilience protocols; checkpoint interval selection and its sensitivity to system parameters for various checkpoint-based fault resilience protocols; and performance comparisons of various promising strategies for fault resilience in exascale-sized systems

Adaptive control in rollforward recovery for extreme scale multigrid

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed algorithm-based recovery method for multigrid iterations by introducing an adaptive control. After a fault, the healthy part of the system continues the iterative solution process, while the solution in the faulty domain is re-constructed by an asynchronous on-line recovery. The computations in both the faulty and healthy subdomains must be coordinated in a sensitive way, in particular, both under and over-solving must be avoided. Both of these waste computational resources and will therefore increase the overall time-to-solution. To control the local recovery and guarantee an optimal re-coupling, we introduce a stopping criterion based on a mathematical error estimator. It involves hierarchical weighted sums of residuals within the context of uniformly refined meshes and is well-suited in the context of parallel high-performance computing. The re-coupling process is steered by local contributions of the error estimator. We propose and compare two criteria which differ in their weights. Failure scenarios when solving up to $6.9\cdot10^{11}$ unknowns on more than 245\,766 parallel processes will be reported on a state-of-the-art peta-scale supercomputer demonstrating the robustness of the method

Reliability for exascale computing : system modelling and error mitigation for task-parallel HPC applications

As high performance computing (HPC) systems continue to grow, their fault rate increases. Applications running on these systems have to deal with rates on the order of hours or days. Furthermore, some studies for future Exascale systems predict the rates to be on the order of minutes. As a result, efficient fault tolerance solutions are needed to be able to tolerate frequent failures. A fault tolerance solution for future HPC and Exascale systems must be low-cost, efficient and highly scalable. It should have low overhead in fault-free execution and provide fast restart because long-running applications are expected to experience many faults during the execution. Meanwhile task-based dataflow parallel programming models (PM) are becoming a popular paradigm in HPC applications at large scale. For instance, we see the adaptation of task-based dataflow parallelism in OpenMP 4.0, OmpSs PM, Argobots and Intel Threading Building Blocks. In this thesis we propose fault-tolerance solutions for task-parallel dataflow HPC applications. Specifically, first we design and implement a checkpoint/restart and message-logging framework to recover from errors. We then develop performance models to investigate the benefits of our task-level frameworks when integrated with system-wide checkpointing. Moreover, we design and implement selective task replication mechanisms to detect and recover from silent data corruptions in task-parallel dataflow HPC applications. Finally, we introduce a runtime-based coding scheme to detect and recover from memory errors in these applications. Considering the span of all of our schemes, we see that they provide a fairly high failure coverage where both computation and memory is protected against errors.A medida que los Sistemas de Cómputo de Alto rendimiento (HPC por sus siglas en inglés) siguen creciendo, también las tasas de fallos aumentan. Las aplicaciones que se ejecutan en estos sistemas tienen una tasa de fallos que pueden estar en el orden de horas o días. Además, algunos estudios predicen que los fallos estarán en el orden de minutos en los Sistemas Exascale. Por lo tanto, son necesarias soluciones eficientes para la tolerancia a fallos que puedan tolerar fallos frecuentes. Las soluciones para tolerancia a fallos en los Sistemas futuros de HPC y Exascale tienen que ser de bajo costo, eficientes y altamente escalable. El sobrecosto en la ejecución sin fallos debe ser bajo y también se debe proporcionar reinicio rápido, ya que se espera que las aplicaciones de larga duración experimenten muchos fallos durante la ejecución. Por otra parte, los modelos de programación paralelas basados en tareas ordenadas de acuerdo a sus dependencias de datos, se están convirtiendo en un paradigma popular en aplicaciones HPC a gran escala. Por ejemplo, los siguientes modelos de programación paralela incluyen este tipo de modelo de programación OpenMP 4.0, OmpSs, Argobots e Intel Threading Building Blocks. En esta tesis proponemos soluciones de tolerancia a fallos para aplicaciones de HPC programadas en un modelo de programación paralelo basado tareas. Específicamente, en primer lugar, diseñamos e implementamos mecanismos “checkpoint/restart” y “message-logging” para recuperarse de los errores. Para investigar los beneficios de nuestras herramientas a nivel de tarea cuando se integra con los “system-wide checkpointing” se han desarrollado modelos de rendimiento. Por otra parte, diseñamos e implementamos mecanismos de replicación selectiva de tareas que permiten detectar y recuperarse de daños de datos silenciosos en aplicaciones programadas siguiendo el modelo de programación paralela basadas en tareas. Por último, se introduce un esquema de codificación que funciona en tiempo de ejecución para detectar y recuperarse de los errores de la memoria en estas aplicaciones. Todos los esquemas propuestos, en conjunto, proporcionan una cobertura bastante alta a los fallos tanto si estos se producen el cálculo o en la memoria.Postprint (published version

A diversity-aware computational framework for systems biology

L'abstract è presente nell'allegato / the abstract is in the attachmen

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

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