For large-scale, nonlinear, time-dependent PDE constrained optimization problems with a 3D spatial domain, reduced methods are a viable algorithmic approach. The computation of reduced gradients by adjoint methods requires the storage of 4D data, which can be quite expensive from both a capacity and bandwidth point of view.

This project investigates lossy compression schemes for storing the state trajectory, based on hierarchical interpolation in adaptively refined meshes as a general predictor. A special focus is on the adaptive control of the quantization error in order not to impede convergence of the optimization algorithms.