发表机构
IMADA, University of Southern Denmark（南丹麦大学IMADA）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对格点场论中信噪比问题，提出变分框架将其转化为输运问题，通过输运构型弥合分布差距，统一了朗之万估计与正则化流方法，并在标量理论中验证。
AI 中文摘要
信噪比问题限制了许多格点计算的范围。我们提出了一个变分框架，将其重新表述为输运问题：信号的损失反映了采样分布与测量可观测量所需分布之间的不匹配，可以通过输运构型来弥合这一差距来减少。最优输运通常通过基于朗之万动力学的随机估计器确定，或通过将其参数化为使用自动微分训练的正则化流来确定。我们讨论了该框架如何将这些方法统一在一个共同的变分原理下，并展示了标量理论的结果。
英文摘要
The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.
