普通神经网络的精确等变性用于晶格多体动力学
Exact Equivariance from Ordinary Neural Networks for Lattice Many-Body Dynamics
- University of Virginia（弗吉尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出用有限群平均的普通多层感知器实现精确等变的晶格多体动力学替代模型，在Falicov--Kimball和Holstein模型中验证了微观精度与大规模模拟能力。
AI中文摘要：
关联电子系统的大规模模拟需要反复评估驱动集体动力学的电子力和跃迁能量。机器学习替代模型缓解了这一瓶颈，但融入对称性通常需要精心设计的描述符或专门的网络架构。我们表明，配备有限群平均的普通多层感知器可以直接从微观构型提供精确等变的替代模型。该构造将对称性强制与内部网络架构分离，并适用于离散和连续晶格自由度。在Falicov--Kimball模型中，它预测了方向性跳跃自由能差异；在Holstein模型中，其不变极限生成了保守的晶格力。与精确对角化的基准测试确立了微观精度和动力学关联的一致性，而大规模模拟恢复了多尺度电荷有序和电荷密度波粗化。这些结果展示了一种可访问、可复用的途径，用于具有有限晶格点群的系统的对称保持多体动力学。
英文摘要：
Large-scale simulations of correlated electron systems require repeated evaluations of the electronic forces and transition energies driving collective dynamics. Machine-learning surrogates alleviate this bottleneck, but incorporating symmetry often involves carefully designed descriptors or specialized network architectures. We show that ordinary multilayer perceptrons equipped with finite-group averaging provide exactly equivariant surrogates directly from microscopic configurations. The construction separates symmetry enforcement from the internal network architecture and applies to both discrete and continuous lattice degrees of freedom. In the Falicov--Kimball model, it predicts directional hopping free-energy differences; in the Holstein model, its invariant limit generates conservative lattice forces. Benchmarks against exact diagonalization establish microscopic accuracy and agreement of dynamical correlations, while large-scale simulations recover multiscale charge ordering and charge-density-wave coarsening. These results demonstrate an accessible, reusable route to symmetry-preserving many-body dynamics for systems with finite lattice point groups.
