Optimal checkpointing for adjoint multistage time-stepping schemes

We consider checkpointing strategies that minimize the number of recomputations needed when performing discrete adjoint computations using multistage time-stepping schemes require computing several substeps within one complete time step. Specifically, we propose two algorithms can generate optimal schedules under weak assumptions. The first is an extension seminal Revolve algorithm adapted to schemes. second algorithm, named CAMS, developed based on dynamic programming, and it requires least compared with other algorithms. CAMS made publicly available in a library bindings C Python. Numerical results show proposed deliver up times speedup classical Revolve. Moreover, discuss utilization mature scientific libraries demonstrate ease workflow. have been adopted by PETSc TSAdjoint library. Their performance has demonstrated large-scale PDE-constrained optimization problem leadership-class supercomputer. This work significant authors’ conference paper (Zhang Constantinescu, 2021).