---
title: "Equivariant Deep Learning in Direct-Product Space for Electronic-Structure Hamiltonian Prediction"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.07695v1"
permalink: "https://feed.astralor.com/items/itm_3561617bb57fbdf84262b196"
published: "2026-11-05T09:19:07.000Z"
score: 62
channel: "tech"
tags: ["推理效率","RAG","Equivariant Deep Learning","Direct-Product Space","Electronic-Structure Hamiltonian Prediction","Most","Hamiltonian"]
---

# Equivariant Deep Learning in Direct-Product Space for Electronic-Structure Hamiltonian Prediction

## 速览

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-prod…

## 关键点

- 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-prod…
- This representation mismatch fragments contiguous Hamiltonian blocks, obscures direct manipulation of orbital couplings, and organizes features into irregular angular-momentum components that require numerous transforma…
- 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…

## 全文

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.

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