  Graph networks are a new machine learning (ML) paradigm that supports both
relational reasoning and combinatorial generalization. Here, we develop
universal MatErials Graph Network (MEGNet) models for accurate property
prediction in both molecules and crystals. We demonstrate that the MEGNet
models outperform prior ML models such as the SchNet in 11 out of 13 properties
of the QM9 molecule data set. Similarly, we show that MEGNet models trained on
$\sim 60,000$ crystals in the Materials Project substantially outperform prior
ML models in the prediction of the formation energies, band gaps and elastic
moduli of crystals, achieving better than DFT accuracy over a much larger data
set. We present two new strategies to address data limitations common in
materials science and chemistry. First, we demonstrate a physically-intuitive
approach to unify four separate molecular MEGNet models for the internal energy
at 0 K and room temperature, enthalpy and Gibbs free energy into a single free
energy MEGNet model by incorporating the temperature, pressure and entropy as
global state inputs. Second, we show that the learned element embeddings in
MEGNet models encode periodic chemical trends and can be transfer-learned from
a property model trained on a larger data set (formation energies) to improve
property models with smaller amounts of data (band gaps and elastic moduli).
