Neural networks as low-cost surrogates for impurity solvers in quantum embedding methods

TL;DR

This paper demonstrates that neural networks can serve as efficient low-cost surrogate models for impurity solvers in quantum embedding methods, reducing computational costs and accelerating simulations.

Contribution

The study shows neural networks can be trained with minimal data to accurately interpolate impurity solver outputs and significantly speed up quantum many-body simulations.

Findings

Neural networks achieve accuracy comparable to CT-QMC within the training data range.

NN outputs provide excellent initial guesses, reducing CT-QMC computation time by up to five times.

Performance drops when extrapolating outside the training distribution, especially at lower temperatures.

Abstract

A promising application of machine learning is the creation of low-cost surrogate models to mitigate computational bottlenecks in quantum many-body simulations. Here, we explore whether a neural network (NN) can be trained in the low-data regime, with one to two orders of magnitude fewer training examples than previous works, as an efficient substitute for the impurity solver in dynamical mean-field theory simulations of correlated electron models. We show that the NN solver achieves accuracy comparable to popular continuous-time quantum Monte Carlo (CT-QMC) impurity solvers when interpolating between samples within the training set. While the NN's performance decreases notably when extrapolating to lower temperatures outside the training distribution, its output still provides an excellent initial guess for input to more accurate CT-QMC impurity solvers, thus accelerating the time to solution up to a factor of five. We discuss our results in the context of rapid phase-space exploration.