How Neural Networks reduce the Fermionic Sign Problem and what we can learn from them

When simulating fermionic quantum systems, non-perturbative Monte Carlo techniques are often the most efficient approach known to date. However, beyond half filling they suffer from the so-called sign problem, i.e. negative "probabilities", so that stochastic sampling becomes infeasible. Recently, considerable progress has been made in alleviating the sign problem by deforming the integration contour of the path integral into the complex plane and applying machine learning to find near-optimal alternative contours. In this talk, I am going to present a particularly successful architecture, based on complex-valued affine coupling layers. Furthermore, I will demonstrate how insight gained from the trained network can be used for simpler analytic approaches.