Accurately predicting the elastic properties of crystalline solids is vital
for computational materials science. However, traditional atomistic scale ab
initio approaches are computationally intensive, especially for studying
complex materials with a large number of atoms in a unit cell. We introduce a
novel data-driven approach to efficiently predict the elastic properties of
crystal structures using SE(3)-equivariant graph neural networks (GNNs). This
approach yields important scalar elastic moduli with the accuracy comparable to
recent data-driven studies. Importantly, our symmetry-aware GNNs model also
enables the prediction of the strain energy density (SED) and the associated
elastic constants, the fundamental tensorial quantities that are significantly
influenced by a material's crystallographic group. The model consistently
distinguishes independent elements of SED tensors, in accordance with the
symmetry of the crystal structures. Finally, our deep learning model possesses
meaningful latent features, offering an interpretable prediction of the elastic
properties.

本文提出了一种基于数据驱动的方法，使用 SE (3) 等变图神经网络高效预测晶体结构的弹性性质，该方法能较准确地预测重要弹性模量和变形能密度以及相应的弹性常数，并提供可解释预测的有意义的潜在特征。

StrainNet：使用 SE（3）- 等变图神经网络预测晶体结构的弹性特性

StrainNet: Predicting crystal structure elastic properties using  SE(3)-equivariant graph neural networks

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry
in science, from classical and quantum physics to computational biology. It
enables robust and accurate prediction under arbitrary reference
transformations. In light of this, great efforts have been put on encoding this
symmetry into deep neural networks, which has been shown to improve the
generalization performance and data efficiency for downstream tasks.
Constructing an equivariant neural network generally brings high computational
costs to ensure expressiveness. Therefore, how to better trade-off the
expressiveness and computational efficiency plays a core role in the design of
the equivariant deep learning models. In this paper, we propose a framework to
construct SE(3) equivariant graph neural networks that can approximate the
geometric quantities efficiently. Inspired by differential geometry and
physics, we introduce equivariant local complete frames to graph neural
networks, such that tensor information at given orders can be projected onto
the frames. The local frame is constructed to form an orthonormal basis that
avoids direction degeneration and ensure completeness. Since the frames are
built only by cross product operations, our method is computationally
efficient. We evaluate our method on two tasks: Newton mechanics modeling and
equilibrium molecule conformation generation. Extensive experimental results
demonstrate that our model achieves the best or competitive performance in two
types of datasets.

本文提出了一种构建 SE (3) 等变图神经网络的框架，该框架可以在保证性能的前提下实现计算效率的提升，并在牛顿力学建模和平衡分子构型生成两个任务中展示了优异的性能。