The adjoint computation of an unsteady nonlinear primal function requires
the full primal trajectory in reverse temporal order. Storing this can exceed
the available memory. In that case, Checkpointing can be used to store the
state only at carefully selected points in time. From there, the forward
computation can be restarted to recompute lost sections of the trajectory
when they are needed during the adjoint computation. This is always a
tradeoff between memory and runtime. The classic and provably optimal way
to do this for a known number of time steps is Revolve, and there are other
algorithms for optimal online checkpointing if the number of steps is unknown
a priori, or for multistage checkpointing if there are multiple layers of
storage, e.g. memory and hard drive.