Approximately uniform online checkpointing
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
State Trajectory Compression for Optimal Control with Parabolic PDEs
SIAM Journal on Scientific Computing
Online checkpointing with improved worst-case guarantees
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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.