Calculations of the strong nuclear interactions, encoded in the theory of Quantum Chromodynamics (QCD), are extraordinarily computationally demanding. Inparticular, the Monte Carlo integration used in lattice field theory calculations in this context suffers from severe signal-to-noise challenges. Complexifying the integration manifold with the complex contour deformation method reduces the variances of observables while guaranteeing the exactness of the results. In this work, we use convolutional neural networks to parametrize the deformed manifolds and demonstrate orders-of-magnitude reduction in the variance of a key observable (the Wilson loop) in a simplified model of QCD in three spacetime dimensions.