用对称性感知的扩散模型加速量子场论采样。
Group-Equivariant Diffusion Models for Lattice Field Theory
- 构建群等变得分网络，保留全局反射、局部旋转和周期平移对称性。
- 在二维ϕ⁴与U(1)格点场论中，生成样本质量显著优于普通模型。
- 适合需要高效高保真采样的物理模拟与计算凝聚态研究者。
在临界点附近，格点量子场论（LQFT）的马尔可夫链蒙特卡洛（MCMC）模拟因临界慢化而效率下降。本文探索基于得分的对称性保持扩散模型，作为二维ϕ⁴与U(1)格点场论的替代采样方法。我们设计了对多种群变换等变的得分网络，包括全局ℤ₂反射、局部U(1)旋转和周期平移𝕋。通过增强训练方案训练网络，显著提升了生成样本的质量。实证表明，该对称性感知模型在样本质量、表达能力和有效样本量方面均优于通用得分网络。
原文摘要 · Abstract (English)
Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional $ϕ^4$ and ${\rm U}(1)$ lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global $\mathbb{Z}_2$ reflections, local ${\rm U}(1)$ rotations, and periodic translations $\mathbb{T}$. The score networks are trained using an augmented training scheme, which significantly improves sample quality in the simulated field theories. We also demonstrate empirically that our symmetry-aware models outperform generic score networks in sample quality, expressivity, and effective sample size.
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