  Generating simulated training data needed for constructing sufficiently
accurate surrogate models to be used for efficient optimization or parameter
identification can incur a huge computational effort in the offline phase. We
consider a fully adaptive greedy approach to the computational design of
experiments problem using gradient-enhanced Gaussian process regression as
surrogates. Designs are incrementally defined by solving an optimization
problem for accuracy given a certain computational budget. We address not only
the choice of evaluation points but also of required simulation accuracy, both
of values and gradients of the forward model. Numerical results show a
significant reduction of the computational effort compared to just
position-adaptive and static designs as well as a clear benefit of including
gradient information into the surrogate training.
