用自学习扩散模型生成格点配置
Lattice Configuration Generation with a Self-Learning Diffusion Model
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中文总结 AI 辅助
研究无需外部蒙特卡罗计算准备数据来训练格点场配置扩散采样器，构建自引导采样器SLDiffusion，在二维紧凑XY模型中自训练，结果显示能量和涡旋密度与独立计算相符，积分自相关时间短，证明可自训练。
中文摘要 AI 辅助
我们表明，无需通过外部蒙特卡罗计算准备训练数据，就能训练用于格点场配置的扩散采样器。从β = 0时的精确采样配置开始，构建自引导采样器SLDiffusion，其中具有固定学习得分的周期性高斯提议在每个β处因噪声水平通过Metropolis - Hastings校正到相同物理目标，仅使用所得链中的重放配置在下一阶段训练得分。在二维紧凑XY模型中，自训练在L = 4时从β = 0.30进行到0.50。在β = 0.5时，L = 4、6、8、12的能量和涡旋密度与独立的混合蒙特卡罗计算结果在1.35σ内相符。L = 8和12时的体积原生再训练改善了提议位移和自相关。所研究的所有体积的能量和涡旋密度的积分自相关时间均保持在2以下。这些结果表明，经Metropolis校正的扩散采样器无需从目标耦合预先抽取配置即可进行自训练。
英文摘要
We show that a diffusion sampler for lattice-field configurations can be self-trained without preparing target-ensemble training configurations using an external Monte Carlo calculation. Starting from exactly sampled configurations at $β=0$, we use action-difference weights to train the score at the next coupling. Proposals from a fixed model are Metropolis-Hastings corrected at every noise level, and the resulting chain supplies training configurations for the next stage. This procedure defines the self-learning diffusion sampler SLDiffusion. In the two-dimensional compact XY model, self-training proceeds from $β=0.30$ to $0.50$ at $L=4$ and extends to $L=6,8,12$ at $β=0.5$. The energy and vortex densities agree with independent Hybrid Monte Carlo calculations within $1.6$ combined standard errors. Their integrated autocorrelation times, measured in stored updates, remain below two at all volumes studied. These results demonstrate a diffusion sampler whose training can be initialized and continued without external target-coupling ensembles.
发表机构
- Tokyo Woman’s Christian University（东京女子基督教大学）
- Kyoto University（京都大学）
- RIKEN Center for Computational Science（理化学研究所计算科学中心）
机构由 AI 辅助整理，请以论文原文为准。
