  A key task in the emerging field of materials informatics is to use machine
learning to predict a material's properties and functions. A fast and accurate
predictive model allows researchers to more efficiently identify or construct a
material with desirable properties. As in many fields, deep learning is one of
the state-of-the art approaches, but fully training a deep learning model is
not always feasible in materials informatics due to limitations on data
availability, computational resources, and time. Accordingly, there is a
critical need in the application of deep learning to materials informatics
problems to develop efficient transfer learning algorithms. The Bayesian
framework is natural for transfer learning because the model trained from the
source data can be encoded in the prior distribution for the target task of
interest. However, the Bayesian perspective on transfer learning is relatively
unaccounted for in the literature, and is complicated for deep learning because
the parameter space is large and the interpretations of individual parameters
are unclear. Therefore, rather than subjective prior distributions for
individual parameters, we propose a new Bayesian transfer learning approach
based on the penalized complexity prior on the Kullback-Leibler divergence
between the predictive models of the source and target tasks. We show via
simulations that the proposed method outperforms other transfer learning
methods across a variety of settings. The new method is then applied to a
predictive materials science problem where we show improved precision for
estimating the band gap of a material based on its structural properties.
