  Graph Neural Networks (GNNs) can predict the performance of an industrial
design quickly and accurately and be used to optimize its shape effectively.
However, to fully explore the shape space, one must often consider shapes
deviating significantly from the training set. For these, GNN predictions
become unreliable, something that is often ignored. For optimization techniques
relying on Gaussian Processes, Bayesian Optimization (BO) addresses this issue
by exploiting their ability to assess their own accuracy. Unfortunately, this
is harder to do when using neural networks because standard approaches to
estimating their uncertainty can entail high computational loads and reduced
model accuracy. Hence, we propose a novel uncertainty-based method tailored to
shape optimization. It enables effective BO and increases the quality of the
resulting shapes beyond that of state-of-the-art approaches.
