Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems
arxiv(2024)
摘要
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.
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