用物理约束扩散模型高效模拟规范场论，突破拓扑冻结难题。
Physics-Conditioned Diffusion Models for Lattice Gauge Theory
- 将随机量子化作为物理条件融入扩散模型采样
- 小耦合常数训练的模型可外推至大耦合区域，避免拓扑冻结
- 无需重训练即可适配不同格点尺寸，适合高能物理模拟
我们开发了用于模拟格点规范场论的扩散模型，将随机量子化显式作为采样时的物理约束。在二维时空的U(1)规范场论中验证了该新型采样器的有效性，发现于小反耦合常数下训练的模型可外推至更大反耦合区域，且未出现拓扑冻结问题。此外，训练好的模型可直接用于不同格点尺寸的配置采样，无需重新训练。通过在生成过程中引入马尔可夫链蒙特卡洛修正的郎之万动力学，确保了生成样本的精确性。相比传统算法如混合蒙特卡洛和朗之万模拟，该方法在采样拓扑量方面效率更高。
原文摘要 · Abstract (English)
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.
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