arXiv cs.AI· Shi Yin, Zujian Dai, Xinyang Pan, Lixin He·· 11 小时前AI 评分29
DP-Learner：在直积空间做等变深度学习，提升电子结构哈密顿量预测
Equivariant Deep Learning in Direct-Product Space for Electronic-Structure Hamiltonian Prediction
AI 导读
DP-Learner 是一个直接在直积空间中对类哈密顿量算符块做消息传递的等变学习框架，无需显式 Clebsch–Gordan 分解即可保持对 SO(3)、SU(2) 和空间反演的等变性。
正文 · 原文
Abstract:Most existing equivariant architectures for Hamiltonian prediction propagate features in direct-sum spaces of irreducible spherical tensors, whereas the target Hamiltonian is naturally an operator block in a direct-product representation over local orbital and spin bases. This representation mismatch fragments contiguous Hamiltonian blocks, obscures direct manipulation of orbital couplings, and organizes features into irregular angular-momentum components that require numerous transformations and are poorly aligned with efficient hardware execution and memory management. To address both the representation mismatch and computational bottleneck, we propose DP-Learner, an equivariant learning framework that performs message passing directly on Hamiltonian-like operator blocks in the direct-product space. Theoretically, we propose Lie-generator-based directional embedding and invariantly weighted left--right products and contractions that preserve equivariance to SO(3), SU(2), and spatial inversions, without explicit Clebsch--Gordan decomposition or inverse reconstruction. Methodologically, we instantiate this principle as a Transformer architecture, in which Hamiltonian-like feature matrices or tensors evolve through equivariant operators in the direct-product space, while non-linear invariant scalar routing controls structured gating over matrix units, directional propagation, attention, and environment-embedded context interactions. We further construct MP-HAM-110K, a large-scale Hamiltonian dataset comprising more than 110,000 material structures covering 68 elements with both Hamiltonian and wavefunction data. Experiments on MP-HAM-110K and Materials-HAM-SOC demonstrate that DP-Learner dramatically improves Hamiltonian prediction accuracy and inference efficiency over the state-of-the-art method.
| Subjects: | Machine Learning (cs.LG); Materials Science (cond-mat.mtrl-sci); Artificial Intelligence (cs.AI); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2611.07695 [cs.LG] |
| (or arXiv:2611.07695v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.07695 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Shi Yin [view email]
[v1]
Thu, 5 Nov 2026 09:19:07 UTC (12,914 KB)
来源：arXiv cs.AI · arxiv.org