  The Green's function Monte Carlo (GFMC) method provides accurate solutions to
the nuclear many-body problem and predicts properties of light nuclei starting
from realistic two- and three-body interactions. Controlling the GFMC
fermion-sign problem is crucial, as the signal-to-noise ratio decreases
exponentially with Euclidean time, requiring significant computing resources.
Inspired by similar scenarios in lattice quantum field theory and spin systems,
in this work, we employ integration contour deformations to improve the GFMC
signal-to-noise ratio. Machine learning techniques are used to select optimal
contours with minimal variance from parameterized families of deformations. As
a proof of principle, we consider the deuteron binding energies and Euclidean
density response functions. We only observe mild signal-to-noise improvement
for the binding energy case. On the other hand, we achieve an order of
magnitude reduction of the variance for Euclidean density response functions,
paving the way for computing electron- and neutrino-nucleus cross-sections of
larger nuclei.
