AI 中文总结
该研究针对材料科学，介绍点群对称感知等变图神经网络（PGEqNN），其滤波器函数与对称感知指标对齐。利用等变网络预测能力所在的平凡子空间，\(A_1\)限制变体在少参数下匹配或超越对应物，得到精度相同的更精简模型。
AI 中文摘要
等变图神经网络已被证明是直接从材料结构推断其性质的有效工具。传统上，这些网络应用时尊重完全的\(O(3)\)等变性，使输入结构的任何旋转或反射在模型输出中都能被体现。然而，原子系统的额外对称性未被利用，且滤波器函数的任何对称性是从完整数据集中隐式学习而非严格强制。在这项工作中，我们为材料科学引入点群对称感知等变图神经网络（PGEqNN），其滤波器函数与对称感知指标对齐以在预测任务中实现更高粒度。通过这种架构，我们表明等变网络对张量弹性和介电数据集的大部分预测能力在于点群适配基的平凡子空间。利用这一点，一个\(A_1\)限制变体在训练更少活跃参数的情况下匹配或优于其全点群和\(SO(3)\)划分的对应物，产生具有相同精度的更精简模型。
英文摘要
Equivariant graph neural networks have proven effective tools for inference of material's properties directly from their structure. Traditionally, these have been applied such that they respect full $O(3)$ equivariance, so that any rotation or reflection of the input structure is respected in the model's output. While this works for general arrangements of atoms, additional symmetries of atomistic systems are left unleveraged. Furthermore, any symmetries of the filter functions are implicitly learned from the full dataset and not strictly enforced. In this work, we introduce point-group symmetry aware equivariant graph neural networks (PGEqNN) for materials science, with filter functions aligned with symmetry-aware indices for greater granularity in predictive tasks. With this architecture, we show that most of the predictive power of equivariant networks for tensorial elastic and dielectric datasets lies in the trivial subspaces of the point-group adapted bases. Exploiting this, an $A_1$-restricted variant matches or improves on its full point-group and $SO(3)$-partitioned counterparts while training fewer active parameters, yielding leaner models of equal accuracy.
