Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems
<|reference_start|>Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems: 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.<|reference_end|>
@article{semler2024adaptive,
    title={Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse
  Problems},
    author={Phillip Semler, Martin Weiser},
    journal={arXiv preprint arXiv:2404.01864},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.01864},
    primaryClass={math.NA cs.NA}
}