标题： 通过在二维施温格模型中使用规范协变流进行精细研磨局部更新 显示英文标题

标题： Fine grinding localized updates via gauge equivariant flows in the 2D Schwinger model

摘要： 目前最先进的离散规范理论模拟基于具有场空间局部变化的马尔可夫链，然而在非常精细的格点间距下，由于规范场的分离拓扑区域，这变得非常困难。混合蒙特卡罗（HMC）算法在较粗的格点间距下非常高效，但会经历不断增加的自相关时间。这使得在接近连续极限的格点QCD模拟即使使用百亿亿次计算也变得不可行。一种可以克服长自相关时间的方法是基于平凡化映射，其中新的规范提案是通过将配置从一个平凡空间映射到目标空间，通过相关的玻尔兹曼因子分布给出。使用规范等变耦合层，可以通过机器学习技术近似该映射。然而，在局部理论和广泛分布的情况下，偏差随着体积而扩大，使得对于现实的盒子尺寸全局更新不可行。在本次会议中，我们将讨论2D施温格模型情况下局部更新的潜力。使用规范等变流映射，可以将局部更新细化到更细的格点间距。基于此，我们将展示使用可扩展的全局校正步骤在精细格点间距下模拟带有动态Nf=2威尔逊费米子的2D施温格模型的结果，并将性能与HMC进行比较。 显示英文摘要

摘要： State-of-the-art simulations of discrete gauge theories are based on Markov chains with local changes in the field space, which however at very fine lattice spacings are notoriously difficult due to separated topological sectors of the gauge field. Hybrid Monte Carlo (HMC) algorithms, which are very efficient at coarser lattice spacings, suffer from increasing autocorrelation times. This makes simulation of lattice QCD close to the continuum infeasible even with exa-scale computing. An approach, which can overcome long autocorrelation times, is based on trivializing maps, where a new gauge proposal is given by mapping a configuration from a trivial space to the target one, distributed via the associated Boltzmann factor. Using gauge equivariant coupling layers, the map can be approximated via machine learning techniques. However the deviations scale with the volume in case of local theories and extensive distributions, rendering a global update unfeasible for realistic box sizes. In this proceeding, we will discuss the potential of localized updates in case of the 2D Schwinger Model. Using gauge-equivariant flow maps, a local update can be fine grained towards finer lattice spacing. Based on this we will present results on simulating the 2D Schwinger Model with dynamical Nf=2 Wilson fermions at fine lattice spacings using scalable global correction steps and compare the performance to the HMC.