  We consider the prediction of general tensor properties of crystalline
materials, including dielectric, piezoelectric, and elastic tensors. A key
challenge here is how to make the predictions satisfy the unique tensor
equivariance to O(3) group and invariance to crystal space groups. To this end,
we propose a General Materials Tensor Network (GMTNet), which is carefully
designed to satisfy the required symmetries. To evaluate our method, we curate
a dataset and establish evaluation metrics that are tailored to the intricacies
of crystal tensor predictions. Experimental results show that our GMTNet not
only achieves promising performance on crystal tensors of various orders but
also generates predictions fully consistent with the intrinsic crystal
symmetries. Our code is publicly available as part of the AIRS library
(https://github.com/divelab/AIRS).
