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

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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