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

Machine learning has demonstrated great power in materials design, discovery,
and property prediction. However, despite the success of machine learning in
predicting discrete properties, challenges remain for continuous property
prediction. The challenge is aggravated in crystalline solids due to
crystallographic symmetry considerations and data scarcity. Here we demonstrate
the direct prediction of phonon density of states using only atomic species and
positions as input. We apply Euclidean neural networks, which by construction
are equivariant to 3D rotations, translations, and inversion and thereby
capture full crystal symmetry, and achieve high-quality prediction using a
small training set of $\sim 10^{3}$ examples with over 64 atom types. Our
predictive model reproduces key features of experimental data and even
generalizes to materials with unseen elements,and is naturally suited to
efficiently predict alloy systems without additional computational cost. We
demonstrate the potential of our network by predicting a broad number of high
phononic specific heat capacity materials. Our work indicates an efficient
approach to explore materials' phonon structure, and can further enable rapid
screening for high-performance thermal storage materials and phonon-mediated
superconductors.

本论文利用欧氏神经网络，输入仅为原子种类和位置，直接预测晶体固体中的声子态密度。通过该方法，可以高效地探索材料的声子结构，并能进一步快速筛选出高性能的热储存材料和声子介导超导体。