An InfoCGAN neural network is trained on 2D square Ising configurations conditioned on the external applied magnetic field and the temperature. The network is composed of two main sub-networks. The generator network learns to generate convincing Ising configurations and the discriminator network learns to discriminate between ‘real’ and ‘fake’ configurations with an additional categorical assignment prediction provided by an auxiliary network. Some of the predicted categorical assignments show agreement with the expected physical phases in the Ising model, the ferromagnetic spin-up and spin down phases as well as the high temperature weak external field phase. Additionally, configurations associated with the crossover phenomena are predicted by the model. The classification probabilities allow for a robust method of estimating the critical temperature in the vanishing field case, showing exceptional agreement with the known physics. This work indicates that a representation learning approach using an adversarial neural network can be used to identify categories that strongly resemble physical phases with no a priori information beyond raw physical configurations and the physical conditions they are subject to. Proper implementation of finite size scaling is essential for a complete machine learning approach in order to bring it in line with established statistical mechanics, which is worthwhile for future study.

在以外部施加的磁场和温度为条件的二维正方形Ising配置上训练InfoCGAN神经网络。该网络由两个主要子网组成。生成器网络学习生成令人信服的Ising配置，而鉴别器网络学习通过辅助网络提供的附加分类分配预测来区分“真实”配置和“伪造”配置。一些预测的类别分配显示出与Ising模型中的预期物理相，铁磁自旋向上和向下旋转相以及高温弱外部场相一致。另外，与交叉现象相关的配置由模型预测。分类概率提供了一种可靠的方法来估算消失场中的临界温度，这与已知的物理学有出众的一致性。这项工作表明，使用对抗神经网络的表示学习方法可以用于识别与物理阶段非常相似的类别，而无需除了原始物理配置及其所受的物理条件之外的先验信息。正确执行有限大小缩放对于完整的机器学习方法至关重要，以便使其与已建立的统计机制保持一致，这值得将来研究。