New Algorithms for Optimal Online Checkpointing
New Algorithms for Optimal Online Checkpointing
复制标题
最佳在线检查点的新算法
DOI：
10.1137/080742439
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Walther
中科院分区：
文献类型：
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作者：
Philipp Stumm;A. Walther
通常，优化时变问题的导数计算是基于伴随微分方程的积分。为此，可能需要了解完整的正向解。在给定函数的后验误差估计中也需要类似的信息。在流动控制领域，特别是在三维问题中，由于存储容量的不足，通常无法跟踪完全正向解。此外，对于许多问题，需要自适应时间步进程序来实现有效的时间集成方案。因此，标准的最优离线检查点策略通常不适用于该框架。在本文中，我们提出了两种用于在线检查点过程的算法，用于动态确定检查点分布。我们证明了这些方法产生的检查点分布要么是最优的，要么是几乎最优的，与最优性只有很小的差距。数值结果强调了理论结果。
Frequently, the computation of derivatives for optimizing time-dependent problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution may be required. Similar information is needed in the context of a posteriori error estimation with respect to a given functional. In the area of flow control, especially for three dimensional problems, it is usually impossible to keep track of the full forward solution due to the lack of storage capacities. Further, for many problems, adaptive time-stepping procedures are needed toward efficient integration schemes in time. Therefore, standard optimal offline checkpointing strategies are usually not well suited in that framework. In this paper we present two algorithms for an online checkpointing procedure that determines the checkpoint distribution on the fly. We prove that these approaches yield checkpointing distributions that are either optimal or almost optimal with only a small gap to optimality. Numerical results underline the theoretical results.