  Generative Adversarial Networks (GANs) have shown immense potential in fields
such as text and image generation. Only very recently attempts to exploit GANs
to statistical-mechanics models have been reported. Here we quantitatively test
this approach by applying it to a prototypical stochastic process on a lattice.
By suitably adding noise to the original data we succeed in bringing both the
Generator and the Discriminator loss functions close to their ideal value.
Importantly, the discreteness of the model is retained despite the noise. As
typical for adversarial approaches, oscillations around the convergence limit
persist also at large epochs. This undermines model selection and the quality
of the generated trajectories. We demonstrate that a simple multi-model
procedure where stochastic trajectories are advanced at each step upon randomly
selecting a Generator leads to a remarkable increase in accuracy. This is
illustrated by quantitative analysis of both the predicted equilibrium
probability distribution and of the escape-time distribution. Based on the
reported findings, we believe that GANs are a promising tool to tackle complex
statistical dynamics by machine learning techniques
