Crystal structure search is a long-standing challenge in materials design. We present a dataset of more than 100,000 structural relaxations of potential battery anode materials from randomized structures using density functional theory calculations. We illustrate the usage of the dataset by training graph neural networks to predict structural relaxations from randomly generated structures. Our models directly predict stresses in addition to forces, which allows them to accurately simulate relaxations of both ionic positions and lattice vectors. We show that models trained on the molecular dynamics simulations fail to simulate relaxations from random structures, while training on our data leads to up to two orders of magnitude decrease in error for the same task. Our model is able to find an experimentally verified structure of a stoichiometry held out from training. We find that randomly perturbing atomic positions during training improves both the accuracy and out of domain generalization of the models.

We introduce tensor field networks, which are locally equivariant to 3D rotations and translations (and invariant to permutations of points) at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate how tensor field networks learn to model simple physics (Newtonian gravitation and moment of inertia), classify simple 3D shapes (trained on one orientation and tested on shapes in arbitrary orientations), and, given a small organic molecule with an atom removed, replace the correct element at the correct location in space.