  The prediction of configurational disorder properties, such as
configurational entropy and order-disorder phase transition temperature, of
compound materials relies on efficient and accurate evaluations of
configurational energies. Previous cluster expansion methods are not applicable
to configurationally-complex material systems, including those with atomic
distortions and long-range orders. In this work, we propose to leverage the
versatile expressive capabilities of graph neural networks (GNNs) for efficient
evaluations of configurational energies and present a workflow combining
attention-based GNNs and Monte Carlo simulations to calculate the disorder
properties. Using the dataset of face-centered tetragonal gold copper without
and with local atomic distortions as an example, we demonstrate that the
proposed data-driven framework enables the prediction of phase transition
temperatures close to experimental values. We also elucidate that the variance
of the energy deviations among configurations controls the prediction accuracy
of disorder properties and can be used as the target loss function when
training and selecting the GNN models. The work serves as a fundamental step
toward a new data-driven paradigm for the accelerated design of
configurationally-complex functional material systems.
