Lossy data compression reduces communication time in hybrid time-parallel integrators

Fischer, Lisa; Götschel, Sebastian; Weiser, Martin

doi:10.1007/s00791-018-0293-2

Cited by 5 publications

(5 citation statements)

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“…The approach used in this article is to select a level of lossy compression that results in an error that is less than the spatial discretization error of the problem. A similar approach to ours is presented in Fischer et al (2017) and uses estimates on simulation accuracy to reduce the communication volume in parallel ODE solvers by compressing floating-point values via truncation. In addition, Fischer et al (2017) prove the stability and convergence of their numerical scheme with the introduced, controlled perturbations during communication.…”

Section: Methodsmentioning

confidence: 99%

“…A similar approach to ours is presented in Fischer et al (2017) and uses estimates on simulation accuracy to reduce the communication volume in parallel ODE solvers by compressing floating-point values via truncation. In addition, Fischer et al (2017) prove the stability and convergence of their numerical scheme with the introduced, controlled perturbations during communication. In this article, we computationally verify our methodology for selecting lossy compression error tolerances.…”

Section: Methodsmentioning

confidence: 99%

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Exploring the feasibility of lossy compression for PDE simulations

Calhoun

Cappello

Olson

et al. 2018

The International Journal of High Performance Computing Applica

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Checkpoint restart plays an important role in high-performance computing (HPC) applications, allowing simulation runtime to extend beyond a single job allocation and facilitating recovery from hardware failure. Yet, as machines grow in size and in complexity, traditional approaches to checkpoint restart are becoming prohibitive. Current methods store a subset of the application's state and exploit the memory hierarchy in the machine. However, as the energy cost of data movement continues to dominate, further reductions in checkpoint size are needed. Lossy compression, which can significantly reduce checkpoint sizes, offers a potential to reduce computational cost in checkpoint restart. This article investigates the use of numerical properties of partial differential equation (PDE) simulations, such as bounds on the truncation error, to evaluate the feasibility of using lossy compression in checkpointing PDE simulations. Restart from a checkpoint with lossy compression is considered for a fail-stop error in two time-dependent HPC application codes: PlasComCM and Nek5000. Results show that error in application variables due to a restart from a lossy compressed checkpoint can be masked by the numerical error in the discretization, leading to increased efficiency in checkpoint restart without influencing overall accuracy in the simulation.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Exploring the feasibility of lossy compression for PDE simulations

Calhoun

Cappello

Olson

et al. 2018

The International Journal of High Performance Computing Applica

View full text Add to dashboard Cite

show abstract

“…If the parallelized application of S is significantly faster than computing a single subtrajectory up to fine grid discretization accuracy, reasonable parallel efficiencies above 0.5 can be achieved [64]. For a fast convergence, however, the terminal values u n (t n+1 ) have to be propagated sequentially as initial values of u n+1 (t n+1 ) over all subintervals during each application of the approximate solver S. Thus, communication time can significantly affect the overall solution time [65]. Compressed communication can therefore improve the time per iteration, but may also impede on the convergence speed and increase the number of iterations.…”

Section: Inexact Parallel-in-time Integratorsmentioning

confidence: 99%

“…Note that this model neglects the impact of inexact checkpoints on the re-computation time, which might increase, e.g., due to iterative methods requiring additional steps to reduce the compression error. For iterative linear solvers this is done in [89]; a thorough analysis for the example of parallel-in-time simulation with hybrid parareal methods can be done along the lines of [65].…”

Section: Checkpoint/restartmentioning

confidence: 99%

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Compression Challenges in Large Scale Partial Differential Equation Solvers

Götschel

Weiser

2019

Algorithms

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Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to relatively small arithmetic intensity, and increasingly so due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers during the last decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to main memory. Exemplarily, we illustrate concepts at particular methods, and give references to alternatives.

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