发表机构
Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对布洛赫态表示中的规范冗余问题，提出$U(1)$等变自编码器，实现高保真压缩并预测$GW$自能，验证规范等变性的关键作用。
AI 中文摘要
平均场布洛赫态的表示学习（或特征化）为将电子信息纳入第一性原理凝聚相系统的机器学习模型提供了一条重要途径。表示布洛赫态的一个挑战是每个态都存在规范冗余。在本工作中，我们提出通过在机器学习框架中显式引入规范等变性来解决这一问题。我们开发了一个$U(1)$等变自编码器，将密度泛函理论获得的平面波基布洛赫态压缩为低维潜在表示。使用二维绝缘体数据集，我们在64维潜在空间中实现了原始波函数与重构之间0.970的平均重叠度。我们进一步表明，$U(1)$等变性赋予潜在空间具有物理意义的结构，包括平滑性和拓扑信息。最后，我们展示了一个原理验证应用，其中潜在表示被用于预测$GW$自能矩阵的非对角元素，并证明了在预测中强制执行规范等变性的重要性。
英文摘要
Representation learning, or featurization, of mean-field Bloch states provides an important route for incorporating electronic information into machine-learning models of first-principles condensed-phase systems. A challenge in representing Bloch states is the gauge redundancy of each state. In this work, we propose to address this issue by explicitly incorporating gauge equivariance in the machine-learning framework. We develop a $U(1)$-equivariant autoencoder that compresses the plane-wave-basis Bloch states obtained from density functional theory into a low-dimensional latent representation. We achieve an average overlap of 0.970 between original wavefunctions and the reconstructions from a 64-dimensional latent space using a dataset of two-dimensional insulators. We further show that $U(1)$ equivariance endows the latent space with physically meaningful structures, including smoothness and topological information. Finally, we present a proof-of-principle application in which the latent representations are used to predict the off-diagonal elements of the $GW$ self energy matrix, and demonstrate the importance of enforcing gauge equivariance in the prediction.
Comments16 pages, 8 figures
