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We consider checkpointing strategies that minimize the number ofrecomputations needed when performing discrete adjoint computations usingmultistage time-stepping schemes, which requires computing several substepswithin one complete time step. In this case we propose two algorithms that cangenerate optimal checkpointing schedules under weak assumptions. The first isan extension of the seminal Revolve algorithm adapted to multistage schemes.The second algorithm, named CAMS, is developed based on dynamic programming,and it requires the least number of recomputations when compared with otheralgorithms. The CAMS algorithm is made publicly available in a library withbindings to C and Python. Numerical results illustrate that the proposedalgorithms can deliver up to two times the speedup compared with that ofclassical Revolve. Moreover, we discuss a tailored implementation of an adjointcomputation that is arguably better suited for mature scientific computinglibraries by avoiding the central control assumed by the original checkpointingstrategy. The proposed algorithms have been adopted by the PETSc TSAdjointlibrary. Their performance has been demonstrated with a large-scalePDE-constrained optimization problem on a leadership-class supercomputer.

Optimal Checkpointing for Adjoint Multistage Time-Stepping Schemes