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Iterative methods are commonly used approaches to solve large, sparse linearsystems, which are fundamental operations for many modern scientificsimulations. When the large-scale iterative methods are running with a largenumber of ranks in parallel, they have to checkpoint the dynamic variablesperiodically in case of unavoidable fail-stop errors, requiring fast I/Osystems and large storage space. To this end, significantly reducing thecheckpointing overhead is critical to improving the overall performance ofiterative methods. Our contribution is fourfold. (1) We propose a novel lossycheckpointing scheme that can significantly improve the checkpointingperformance of iterative methods by leveraging lossy compressors. (2) Weformulate a lossy checkpointing performance model and derive theoretically anupper bound for the extra number of iterations caused by the distortion of datain lossy checkpoints, in order to guarantee the performance improvement underthe lossy checkpointing scheme. (3) We analyze the impact of lossycheckpointing (i.e., extra number of iterations caused by lossy checkpointingfiles) for multiple types of iterative methods. (4)We evaluate the lossycheckpointing scheme with optimal checkpointing intervals on a high-performancecomputing environment with 2,048 cores, using a well-known scientificcomputation package PETSc and a state-of-the-art checkpoint/restart toolkit.Experiments show that our optimized lossy checkpointing scheme cansignificantly reduce the fault tolerance overhead for iterative methods by23%~70% compared with traditional checkpointing and 20%~58% compared withlossless-compressed checkpointing, in the presence of system failures.

Improving Performance of Iterative Methods by Lossy Checkponting