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.

翻译：生成对抗网络（GANs）在远离物理学的领域（如文本和图像生成）已展现出巨大潜力。本文利用GANs学习晶格上的典型随机过程。通过对原始数据适当添加噪声，我们成功使生成器和判别器的损失函数均接近其理想值。然而，作为对抗性方法的典型特征，振荡现象依然存在。这影响了模型选择以及所生成轨迹的质量。我们证明，一种合适的随机轨迹推进策略（每一步随机选取生成器进行推进）的多模型方法能够显著提升精度。基于上述发现，GANs有望成为处理复杂统计动力学的有力工具。