  Graph neural networks, trained on experimental or calculated data are
becoming an increasingly important tool in computational materials science.
Networks, once trained, are able to make highly accurate predictions at a
fraction of the cost of experiments or first-principles calculations of
comparable accuracy. However these networks typically rely on large databases
of labelled experiments to train the model. In scenarios where data is scarce
or expensive to obtain this can be prohibitive. By building a neural network
that provides a confidence on the predicted properties, we are able to develop
an active learning scheme that can reduce the amount of labelled data required,
by identifying the areas of chemical space where the model is most uncertain.
We present a scheme for coupling a graph neural network with a Gaussian process
to featurise solid-state materials and predict properties \textit{including} a
measure of confidence in the prediction. We then demonstrate that this scheme
can be used in an active learning context to speed up the training of the
model, by selecting the optimal next experiment for obtaining a data label. Our
active learning scheme can double the rate at which the performance of the
model on a test data set improves with additional data compared to choosing the
next sample at random. This type of uncertainty quantification and active
learning has the potential to open up new areas of materials science, where
data are scarce and expensive to obtain, to the transformative power of graph
neural networks.
