In this work, we study generative adversarial networks (GANs) as a tool to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters or other quantities associated with individual configurations. For concreteness, we focus on two examples of conditional variables---the temperature of the system and the energy of the samples. We show that temperature-conditioned models can not only be used to generate samples across thermal phase transitions, but also be employed as unsupervised indicators of transitions. To this end, we introduce a GAN-fidelity measure that captures the model’s susceptibility to external changes of parameters. The proposed energy-conditioned models are integrated with Monte Carlo simulations to perform over-relaxation steps, which break the Markov chain and reduce auto-correlations. We propose ways of efficiently representing the physical states in our network architectures, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. A detailed evaluation, using the two-dimensional XY model as an example, shows that these incorporations bring in considerable improvements over standard machine-learning approaches. We further study the performance of our architectures when no training data is provided near the critical region.

中文翻译：

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自旋系统中采样和相变指示的条件生成模型

在这项工作中，我们研究了生成对抗网络 (GAN) 作为一种工具来学习自旋配置的分布并生成样本，条件是外部调整参数或与个人配置相关的其他数量。为了具体起见，我们关注两个条件变量的例子——系统温度和样本能量。我们表明，温度条件模型不仅可以用于生成跨越热相变的样本，还可以用作无监督的转变指标。为此，我们引入了一种 GAN 保真度度量，用于捕捉模型对外部参数变化的敏感性。提出的能量条件模型与蒙特卡罗模拟相结合以执行过度松弛步骤，这打破了马尔可夫链并减少了自相关。我们提出了在我们的网络架构中有效表示物理状态的方法，例如，通过利用对称性，并最小化生成样本之间的相关性。以二维 XY 模型为例进行的详细评估表明，与标准机器学习方法相比，这些合并带来了相当大的改进。当在关键区域附近没有提供训练数据时，我们进一步研究了我们架构的性能。表明这些合并比标准机器学习方法带来了相当大的改进。当在关键区域附近没有提供训练数据时，我们进一步研究了我们架构的性能。表明这些合并比标准机器学习方法带来了相当大的改进。当在关键区域附近没有提供训练数据时，我们进一步研究了我们架构的性能。