Evaluating the Impact of SDC on the GMRES Iterative Solver

Abstract

Abstract-Increasing parallelism and transistor density, along with increasingly tighter energy and peak power constraints, may force exposure of occasionally incorrect computation or storage to application codes. Silent data corruption (SDC) will likely be infrequent, yet one SDC suffices to make numerical algorithms like iterative linear solvers cease progress towards the correct answer. Thus, we focus on resilience of the iterative linear solver GMRES to a single transient SDC. We derive inexpensive checks to detect the effects of an SDC in GMRES that work for a more general SDC model than presuming a bit flip. Our experiments show that when GMRES is used as the inner solver of an inner-outer iteration, it can "run through" SDC of almost any magnitude in the computationally intensive orthogonalization phase. That is, it gets the right answer using faulty data without any required roll back. Those SDCs which it cannot run through, get caught by our detection scheme.

Coping with silent and fail-stop errors at scale by combining replication and checkpointing

“…Bridges et al [30] propose linear solvers to tolerant soft faults using selective reliability. Elliot et al [22] design a fault-tolerant GMRES capable of converging despite silent errors. Bronevetsky and de Supinski [11] provide a comparative study of detection costs for iterative methods.…”

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

“…Bridges et al [34] propose linear solvers to tolerant soft faults using selective reliability. Elliot et al [35] design a fault-tolerant GMRES capable of converging despite latent errors. Bronevetsky and de Supinski [36] provide a comparative study of detection costs for iterative methods.…”

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“…As mentioned in previous sections, the risk of silent data corruptions is increasing. Several studies have explored the impact of SDCs in execution results [16,43,73]. These studies show that a majority of SDCs leads to noticeable impacts such as crashes and hangs but that only a small fraction of them 5 Accuracy here is defined as the prediction recall: the number of correctly predicted failures divided by the number of actual failures Toward Exascale Resilience: 2014 update actually corrupt the results.…”