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Dyson-Schwinger equations (DSEs) are a non-perturbative way to expressn-point functions in quantum field theory. Working in Euclidean space and inLandau gauge, for example, one can study the quark propagator Dyson-Schwingerequation in the real and complex domain, given that a suitable and tractabletruncation has been found. When aiming for solving these equations in thecomplex domain, that is, for complex external momenta, one has to deform theintegration contour of the radial component in the complex plane of the loopmomentum expressed in hyper-spherical coordinates. This has to be done in orderto avoid poles and branch cuts in the integrand of the self-energy loop. Sincethe nature of Dyson-Schwinger equations is such, that they have to be solved ina self-consistent way, one cannot analyze the analytic properties of theintegrand after every iteration step, as this would not be feasible. In theseproceedings, we suggest a machine learning pipeline based on deep learning (DL)approaches to computer vision (CV), as well as deep reinforcement learning(DRL), that could solve this problem autonomously by detecting poles and branchcuts in the numerical integrand after every iteration step and by suggestingsuitable integration contour deformations that avoid these obstructions. Wesketch out a proof of principle for both of these tasks, that is, the pole andbranch cut detection, as well as the contour deformation.

A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations