Metallic Glasses (MGs) are widely used disordered materials. Understanding
the relationship between the local structure and physical properties of MGs is
one of the greatest challenges for both material science and condensed matter
physics. In this work, we utilize Graph Neural Networks (GNNs) to model the
atomic graph structure and study the connection between the structure and the
corresponding local energy barrier, which is believed to govern many critical
physical properties in MGs. One of our key contributions is to propose a novel
Symmetrized GNN (SymGNN) model for predicting the energy barriers, which is
invariant under orthogonal transformations of the structure, e.g., rotations
and reflections. Such invariance is a desired property that standard GNNs like
Graph Convolutional Networks cannot capture. SymGNNs handle the invariance by
aggregating over orthogonal transformations of the graph structure for
representation learning, and an optimal distribution over all 3D orthogonal
transformations $\mathcal{O}_3$ is learned to maximize the benefit of
invariance. We demonstrate in our experiments that SymGNN can significantly
improve the energy barrier prediction over other GNNs and non-graph machine
learning models. With such an accurate model, we also apply graph explanation
algorithms to better reveal the structure-property relationship of MGs. Our GNN
framework allows effective prediction of material physical properties and
bolsters material science research through the use of AI models.

利用图神经网络模型原子图结构，并研究结构与相应的局部能垒之间的关系，以改善金属玻璃材料物理性质的预测，并应用图解释算法揭示金属玻璃材料的结构 - 性质关系。

基于图神经网络的金属非晶体能垒预测与解读

Predicting and Interpreting Energy Barriers of Metallic Glasses with  Graph Neural Networks

Empirical studies on the landscape of neural networks have shown that
low-energy configurations are often found in complex connected structures,
where zero-energy paths between pairs of distant solutions can be constructed.
Here we consider the spherical negative perceptron, a prototypical non-convex
neural network model framed as a continuous constraint satisfaction problem. We
introduce a general analytical method for computing energy barriers in the
simplex with vertex configurations sampled from the equilibrium. We find that
in the over-parameterized regime the solution manifold displays simple
connectivity properties. There exists a large geodesically convex component
that is attractive for a wide range of optimization dynamics. Inside this
region we identify a subset of atypically robust solutions that are
geodesically connected with most other solutions, giving rise to a star-shaped
geometry. We analytically characterize the organization of the connected space
of solutions and show numerical evidence of a transition, at larger constraint
densities, where the aforementioned simple geodesic connectivity breaks down.

研究了负球面感知器模型中的能量壁垒、简单连接性质和优化动力学，并通过计算和数值模拟表征了解决方案空间的组织结构和转换过程。