Generative Adversarial Networks (GANs) have shown immense potential in fields
far from physics, such as in text and image generation. Here we use GANs to
learn 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. However, as typical
for adversarial approaches, oscillations persist. This undermines model
selection and the quality of the generated trajectory. We demonstrate that a
suitable multi-model procedure where stochastic trajectories are advanced at
each step upon randomly selecting a Generator leads to a remarkable increase in
accuracy. Based on the reported findings GANs appears as a promising tool to
tackle complex statistical dynamics.

本研究中我们使用生成对抗网络（GANs）学习格点上原型随机过程，并通过合适的噪声添加成功地使生成器和判别器的损失函数接近最优值。然而，典型的对抗式方法中振荡仍然存在，这损害了模型选择和生成轨迹的质量。我们演示了使用随机生成器推进随机轨迹的适当的多模型程序，可以显著提高精度。基于报告的发现，GANs 是解决复杂统计动力学的有前途的工具。