Interpolation-Restart Strategies for Resilient Eigensolvers

Agullo, Emmanuel; Giraud, Luc; Salas, Pablo; Zounon, Mawussi

doi:10.1137/15m1042115

Cited by 10 publications

(7 citation statements)

References 33 publications

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“…This basic idea can be adapted to more sophisticated linear solvers based on Krylov subspace methods (Agullo et al, 2016a; Langou et al, 2007) or to eigensolvers (Agullo et al, 2016b) and more robust interpolation can be designed to tackle the possible singularity of the diagonal block AIp,Ip−1. We refer to Section 4.1 for a more detailed description of these ideas in the context of the GMRES method.…”

Section: Resilience Methodologiesmentioning

confidence: 99%

“…Interpolation-Restart (IR) techniques are designed to cope with node crashes (hard faults) in a parallel distributed environment (Agullo et al, 2015(Agullo et al, , 2017(Agullo et al, , 2016a(Agullo et al, , 2016b. The methods can be designed at the algebraic level for the solution both of linear systems and of eigenvalue problems.…”

Section: Interpolation-restartmentioning

confidence: 99%

“…We thank the authors of Agullo et al (2016aAgullo et al ( , 2016b, namely E Agullo, L Giraud, A Guermouche, J Roman, P Salas, and M Zounon, for the permission to report the The International Journal of High Performance Computing Applications XX(X) in 2009. His research interests include high-order spectral/hp element methods, software resilience and machine learning, with applications in fluid dynamics and biomedicine.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…We thank the authors of Agullo et al (2016a, 2016b), namely E Agullo, L Giraud, A Guermouche, J Roman, P Salas, and M Zounon, for the permission to report the description and numerical testing of the interpolation-restart strategy in Sections 3.4 and 4, and Dr Christian Kühnlein for the data on solver share of wall-clock time in dynamical core runs. PDD gratefully acknowledges funding from the Royal Society for his University Research Fellowship.…”

Section: Acknowledgementsmentioning

confidence: 99%

See 3 more Smart Citations

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Benacchio

Bonaventura

Altenbernd

et al. 2021

The International Journal of High Performance Computing Applica

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Progress in numerical weather and climate prediction accuracy greatly depends on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increased average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys hardware, application-level and algorithm-level resilience approaches of particular relevance to time-critical numerical weather and climate prediction systems. A selection of applicable existing strategies is analysed, featuring interpolation-restart and compressed checkpointing for the numerical schemes, in-memory checkpointing, user-level failure mitigation and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analysed and some recommendations outlined for future developments.

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Section: Resilience Methodologiesmentioning

confidence: 99%

Section: Interpolation-restartmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

See 2 more Smart Citations

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Benacchio

Bonaventura

Altenbernd

et al. 2021

The International Journal of High Performance Computing Applica

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show abstract

“…These trade-offs can naturally be applied to the interpolations we use, if needed. Agullo et al have further extended restart recoveries relying on lost data interpolation to eigensolvers [1].…”

Section: Checkpointless Algebraic Recoveriesmentioning

confidence: 99%

Asynchronous and Exact Forward Recovery for Detected Errors in Iterative Solvers

Jaulmes¹,

Moretó²,

Ayguadé³

et al. 2018

IEEE Trans. Parallel Distrib. Syst.

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Abstract-Current trends and projections show that faults in computer systems become increasingly common. Such errors may be detected, and possibly corrected transparently, e.g. by Error Correcting Codes (ECC). For a program to be fault-tolerant, it needs to also handle the Errors that are Detected and Uncorrected (DUE), such as an ECC encountering too many bit flips in a codeword. While correcting an error has an overhead in itself, it can also affect the progress of a program. The most generic technique, rolling back the program state to a previously taken checkpoint, sets back any progress done since then. Alternately, application specific techniques exist, such as restarting an iterative program with its latest iteration's values as initial guess. We introduce a novel error correction technique for iterative linear solvers, designed to preserve both the progress made and the solver's future convergence by recovering the program's state exactly. Leveraging the asynchrony of task-based programming models, we mask our technique's overhead by overlapping error correction with the solver's normal workload. Our technique relies on analysing solvers to find redundancy in the form of relations between data. We are then able to restore discarded or corrupted data by recomputing or inverting the appropriate relations. We demonstrate that this approach allows to recover any part of three widely used Krylov subspace methods: CG, GMRES and BiCGStab, and their pre-conditioned versions. We implement our technique for CG and recover lost data at the scale of a memory page, which is the granularity at which Operating Systems (OS) report memory errors on commodity hardware, and study the effect of varying the memory page size to address non-standard sizes and the possible use of huge pages in High Performance Computing (HPC). When compared to checkpointing and to the state-of-the-art algorithmic restart technique, on small (8 cores) to large scale (1024 cores), our methods show less overhead. A trade-off arises between our straightforward and asynchronous approaches, based on the rate at which faults happen. At the lowest considered rate and page size, overlapping recoveries decreases their average cost from 5.40% to 2.24% of the ideal faultless execution time. Our methods generally outperform the state-of-the-art even with increased overheads on big page sizes, and perform similarly on edge cases. These results also indicate that our techniques are increasingly efficient as the matrix size increases.

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Towards Local-Failure Local-Recovery in PDE Frameworks: The Case of Linear Solvers

Altenbernd

Dreier

Engwer

et al. 2021

Lecture Notes in Computer Science

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Interpolation-Restart Strategies for Resilient Eigensolvers

Cited by 10 publications

References 33 publications

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Asynchronous and Exact Forward Recovery for Detected Errors in Iterative Solvers

Towards Local-Failure Local-Recovery in PDE Frameworks: The Case of Linear Solvers

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