Machine learning of Kondo physics using variational autoencoders and symbolic regression

TL;DR

This paper uses variational autoencoders and symbolic regression to analyze Anderson impurity model spectral data, uncovering interpretable features and rediscovering the Kondo temperature formula, demonstrating a general approach for physical insight extraction.

Contribution

It introduces a machine learning pipeline combining variational autoencoders and symbolic regression to extract and interpret physical parameters from spectral data.

Findings

Latent variables correlate with known physical parameters.

The Kondo temperature formula was rediscovered through symbolic regression.

The approach is generalizable to other physical systems.

Abstract

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.