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

翻译：生成对抗网络（GANs）在文本和图像生成领域展现出巨大潜力。直到最近，才有研究尝试将GANs应用于统计力学模型。本文通过将GANs应用于晶格上的典型随机过程，对该方法进行了定量检验。通过在原始数据中适当添加噪声，我们成功使生成器和判别器的损失函数接近其理想值。重要的是，尽管引入了噪声，模型的离散性仍得以保留。与对抗方法的典型特征一致，在较大训练轮次后，围绕收敛极限的振荡仍然持续存在，这影响了模型选择及生成轨迹的质量。我们证明，一种简单的多模型过程——即在每一步随机选取一个生成器来推进随机轨迹——可显著提升精度。通过对预测平衡概率分布和逃逸时间分布的定量分析，该优势得到了验证。基于上述发现，我们认为GANs是借助机器学习技术处理复杂统计动力学问题的一种有前景的工具。