Enhancing diagrammatic Monte Carlo via machine learning

Since their introduction in 1949 Feynman's diagrams have proven over time to be the most precise and intuitive way of approaching quantum field theory, quantum statistical mechanics, and many-body physics. Feynman's diagrams approach is used in many physical problems, as they are able to simplify complex formalism and provide efficient tools for numerical simulations. The Diagrammatic Monte Carlo (DMC) technique is one such computational methods, which stands tall among the most precise approximation-free Markov Chain integration methods. Still, As all Monte Carlo approaches, the main limitation of DMC is the huge computational cost. Thus, in this thesis work, we aimed to reduce the computational time by proposing new ways of constructing the diagrams Markov Chain to reduce correlation with respect to today's standard approaches. This study has led us to the creation of two new proposals: an analytical approach that grants the minimum correlation possible in the Markov Chain, and a more general neural network protocol based on the Normalizing Flow architecture. Both methods have been tested on different models showing effectiveness in reducing the correlation, and so the number of samples needed for convergence, giving a boost in performances if used in the proper context.