@inproceedings{SemlerWeiser2025, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive gradient-enhanced Gaussian process surrogates for inverse problems}, booktitle = {Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023}, editor = {Fackeldey, Konstantin and Kannan, Aswin and Pokutta, Sebastian and Sharma, Kartikey and Walter, Daniel and Walther, Andrea and Weiser, Martin}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/2404.01864}, doi = {10.1515/9783111376776-005}, pages = {59 -- 78}, year = {2025}, abstract = {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.}, language = {en} }