Abstract
We discuss complexity issues in time dependent adjoint evaluation. We address the question of storage complexity and redundant calculation of intermediate states in adjoint calculations for time dependent flows. Parallel in time solutions are introduced in reverse time integration together with reduced order modelling for the recovery of intermediate forward states between checkpoints. The approach is illustrated on an identification problem from partial macroscopic variables fields observations and also in the context of shape sensitivity evaluation in fluids for the pressure and viscous drag coefficients.