Machine learning methods for generation of random images and equilibrated configurations of gluon fields in Quantum Chromodynamics

量子色动力学的模拟是物理学中最具挑战性的计算问题之一，通常使用并行计算，硬件加速，超大数据集的高级统计分析和低级代码优化。蒙特-卡罗模拟的一个最重要的挑战是平衡和去关联胶子场的组态，使它们的定态分布再现QCD的玻尔兹曼重量。这需要对胶子场进行复杂的非局部更新。我利用变分自编码器（VAE）和生成对抗网络（GAN）等神经网络来学习最有效的非局部更新，从而实现量子场系综的最快平衡和热化。我评估了这些方法与传统方法在计算资源方面的使用，然后应用这些算法的发展来解决有关强子物质可能的奇异相的悬而未决的问题，如中子星星内核中极致密核物质可能的超流性和色超导性。我研究了输运系数如电导率和粘度对两个-色QCD在非零夸克密度。输运系数直接用于夸克-胶子等离子体的流体力学模拟，并在解释LHC和RHIC对撞机上重离子碰撞实验中强子和轻子产生的实验结果中发挥重要作用。本文应用格点QCD中的蒙特-卡罗方法研究了具有强关联电子的凝聚态系统

Simulations of Quantum Chromodynamics are among the most challenging computational problems in physics, and typically use parallel computing, hardware acceleration, advanced statistical analysis of very large datasets, and low-level code optimization. One of the most important challenges for Monte-Carlo simulations is to equilibrate and de-correlate configurations of gluon fields, so that their stationary distribution reproduces the Boltzmann weight of QCD. This requires complex, non-local updates of gluon fields.I utilise neural networks such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) to learn the most efficient non-local updates that lead to fastest equilibration and thermalization of ensembles of quantum fields. I evaluate the use of these methods vs traditional methods in terms of computing resources.I then apply these algorithmic developments to address outstanding questions about possible exotic phases of hadronic matter, such as possible superfluidity and colour superconductivity of extremely dense nuclear matter in neutron star cores.I study the dependence of transport coefficients such as electric conductivity and viscosity on fermion density within two-colour QCD at nonzero quark density. Transport coefficients directly feed into hydrodynamic simulations of quark-gluon plasma, and play an important role in the interpretation of experimental results on hadron and lepton production in heavy ion collision experiments on LHC and RHIC colliders. I apply Monte-Carlo methods used in lattice QCD to study condensed matter systems with strongly correlated electrons