Parallel-in-time: A comment by M. Hinze and T. Slawig
In high-performance computing and nowadays’ computing facilities, the number of cores has increased rapidly in the last years, and will do so further in the future. In contrast, the speed of each single core does not grow rapidly any more. Thus, the exploitation of parallelism becomes a crucial point in every design of simulation software where high computational effort is needed. This naturally refers to climate simulations, may these be predictions or paleo runs as in PalMod.
The setting in paleo-computing is special because of two facts: At first, the spatial resolution is numerically coupled with the time-step due to stability conditions. Secondly, the needed long time horizons prohibit short time-steps, and thus restrict also the spatial resolution.
As result, the high number of available cores cannot be used to accelerate the overall computation time. They may nevertheless be used to perform parallel ensemble and sensitivity experiments.
The concept of time-parallelism allows to exploit more and more hardware cores.
For us human beings, the idea of parallelizing the time sounds crude in the first place.
We have a very sequential sense of “time”. Also for climate scientists the concept might be somehow weird, since steps in a model are typically connected with a time-step (of 80 seconds or 3 hours, a day or a year).
The parallel-in-time method breaks this intuitively clear and familiar concept: Here steps in the algorithm only partly reflect an actual step from one time instant to another. Contrarily, the steps of a parallel-in-time algorithm are internal steps on the way towards the final solution, which gives a continuous trajectory at the end of the computation.
In several research papers, it can already be seen that also problems with different internal time scales or including chaotic behavior (e.g. the Lorenz system) can be treated with this method.
However, applying the parareal method to the PalMod setting still is a challenge, since it has to be implemented using the available Earth System Models. Here, several options are thinkable: Coupling between different spatial resolutions as well as the usage of simpler reduced or intermediate complexity models. In this context, the parareal method is a mathematical key enabler for faster climate simulations and with this perfectly fits to the ambitious goal of the PalMod project. Currently the parareal method is implemented in the simulation environment of WG 4.3.
 SIAM News May 2017: https://sinews.siam.org/Details-Page/climate-prediction-exascale-computing-and-time-parallelism