We employ variational autoencoders to extract physical insight from a dataset of one-particle Anderson impurity model spectral functions. Autoencoders are trained to find a low-dimensional, latent space representation that faithfully characterizes each element of the training set, as measured by a reconstruction error. Variational autoencoders, a probabilistic generalization of standard autoencoders, further condition the learned latent space to promote highly interpretable features. In our study, we find that the learned latent variables strongly correlate with well known, but nontrivial, parameters that characterize emergent behaviors in the Anderson impurity model. In particular, one latent variable correlates with particle-hole asymmetry, while another is in near one-to-one correspondence with the Kondo temperature, a dynamically generated low-energy scale in the impurity model. Using symbolic regression, we model this variable as a function of the known bare physical input parameters and "rediscover" the non-perturbative formula for the Kondo temperature. The machine learning pipeline we develop suggests a general purpose approach which opens opportunities to discover new domain knowledge in other physical systems.
翻译:我们使用变式自动编码器从单粒子Anderson杂质模型光谱功能的数据集中获取物理洞察力。 自动编码器受过训练, 以找到一个低维、 潜潜伏的空间代表, 以重建错误来测量训练组中每个元素的真实特征 。 变式自动编码器, 标准自动编码器的概率化一般化, 进一步为学习到的潜伏空间提供条件, 以推广高度可解释的特征 。 在我们的研究中, 我们发现, 所学到的潜伏变量与在安德森杂质模型中出现的行为特征的已知但非三维的参数密切相关。 特别是, 一个与粒子孔不对称的潜伏变量相关, 而另一个则与 Kondo 温度相近一对一对一的动态生成的低能量尺度 。 使用符号回归, 我们将这个变量作为已知的光物理输入参数和 Kondo 温度的非扰动式公式的函数进行模拟。 我们开发的机器学习管道显示一种一般目的方法, 开启在其它物理系统中发现新域知识的机会 。