A Machine Learning Approach for Lattice Gauge Fixing
University of Tsukuba（筑波大学）；Tokyo Woman’s Christian University（东京女子基督教大学）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Kyoto University（京都大学）
Ho Hsiao, Benjamin J. Choi, Hiroshi Ohno, Akio Tomiya
备注：
10 pages, 4 figures, 2 tables, Proceedings of the 42nd International Symposium on Lattice Field Theory (Lattice 2025), November 2nd - 8th, 2025, TIFR Mumbai, India
Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling bottlenecks on large lattices. We present a novel machine learning framework for lattice gauge fixing, where Wilson lines are utilized to construct gauge transformation matrices within a convolutional neural network. The model parameters are optimized via backpropagation, and we introduce a hybrid strategy that combines a neural-network-based transformation with subsequent iterative methods. Preliminary tests on SU(3) gauge theory ensembles for Coulomb gauge demonstrate the potential of this approach to improve the efficiency of lattice gauge fixing. Furthermore, we show that the model exhibits lattice size transferability, where parameters optimized on smaller lattices remain effective for larger volumes without additional training. This framework provides a scalable path toward mitigating critical slowing down in high-precision gauge fixing.
本文提出了一种新的规范固定到标准格点朗道规范的方法，Max Re Tr $\sum_{μ,x}U_{μ,x}$，在该方法中，对链组态进行递归涂抹，然后用标准极值化方法对这些涂抹的链进行规范固定.生成的规范变换同时应用于原始链接。在此预处理之后，像往常一样再次对连杆进行量规固定。这种方法不需要Gribov拷贝，并且我们发现对于物理参数（SU（2）中的$β\geq 2$），它通常会得到具有全局最大迹的规范固定位形。该方法是寻找全局优化问题唯一最小值的通用技术。
Landau Gauge Fixing supported by Genetic Algorithm
提出了一类朗道规范固定的算法，该算法利用遗传算法的思想使最速上升法（SA法）更有效。主要关注的是如何将随机规范变换（RGT）%，变异的遗传算法（GA）的术语，以获得更高的最小朗道规范固定的成就，并保持较低的时间消耗。其中一种算法采用分块RGT，另一种算法采用局部适应度密度控制的RGT，最后一种算法采用Ising Monte Carlo过程确定的RGT。我们测试了这些算法在SU（2）格点规范理论在4维小$β$ s，2.0，1.75和1.5，并报告改进命中率和/或在时间消耗，与其他方法相比。
Exploring gauge-fixing conditions with gradient-based optimization
Center for Theoretical Physics, Massachusetts Institute of Technology（麻省理工学院理论物理中心）；The NSF AI Institute for Artificial Intelligence（美国国家科学基金会人工智能研究所）；Albert Einstein Center, Institute for Theoretical Physics, University of Bern（伯尔尼大学阿尔伯特·爱因斯坦中心理论物理研究所）；Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）；Fermi National Accelerator Laboratory（费米国家加速器实验室）
Toward precise $ξ$ gauge fixing for the lattice QCD
School of Physics, Dalian University of Technology（大连理工大学物理学院）；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理学院）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences, School of Physical Sciences（中国科学院大学物理科学学院）；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学科学中心）；International Centre for Theoretical Physics Asia-Pacific（亚太理论物理中心）
