用扩散模型模拟非阿贝尔规范场论，精度高且泛化能力强。
Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory
- 基于晶格规范等变卷积网络，保持晶格局部与全局对称性。
- 仅需单个蒙特卡洛样本训练，即可在更大耦合强度和晶格尺寸下保持高精度。
- 适合研究规范场论中的拓扑性质与大尺度物理行为。
我们证明了规范等变扩散模型可借助马尔可夫调整退火朗之万算法（MAALA），准确建模二维U(2)与SU(2)规范理论的物理现象。网络架构采用晶格规范等变卷积神经网络（L-CNNs），在晶格上尊重局部与全局对称性。模型仅在传统蒙特卡洛方法生成的单一系综上训练。通过研究不同尺寸的威尔逊环及拓扑易感度，发现该扩散方法在更大逆耦合常数与晶格尺寸下仍具有优异泛化能力，精度损失极小，同时维持中等偏高的接受率。
原文摘要 · Abstract (English)
We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.
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