Machine learning of Kondo physics using variational autoencoders and symbolic regression
This work provides a general-purpose machine learning approach for discovering domain knowledge in physical systems, though it is incremental as it applies existing methods to a known model.
The authors tackled the problem of extracting physical insights from spectral functions of the Anderson impurity model by using variational autoencoders and symbolic regression, resulting in the rediscovery of the non-perturbative formula for the Kondo temperature through learned latent variables that correlate with key physical parameters.
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.