  The elasticity tensor that describes the elastic response of a material to
external forces is among the most fundamental properties of materials. The
availability of full elasticity tensors for inorganic crystalline compounds,
however, is limited due to experimental and computational challenges. Here, we
report the materials tensor (MatTen) model for rapid and accurate estimation of
the full fourth-rank elasticity tensors of crystals. Based on equivariant graph
neural networks, MatTen satisfies the two essential requirements for elasticity
tensors: independence of the frame of reference and preservation of material
symmetry. Consequently, it provides a unified treatment of elasticity tensors
for all seven crystal systems across diverse chemical spaces, without the need
to deal with each separately.. MatTen was trained on a dataset of
first-principles elasticity tensors garnered by the Materials Project over the
past several years (we are releasing the data herein) and has broad
applications in predicting the isotropic elastic properties of polycrystalline
materials, examining the anisotropic behavior of single crystals, and
discovering new materials with exceptional mechanical properties. Using MatTen,
we have discovered a hundred new crystals with extremely large maximum
directional Young's modulus and eleven polymorphs of elemental cubic metals
with unconventional spatial orientation of Young's modulus.
