Machine learning approach for vibronically renormalized electronic band structures

TL;DR

This paper introduces a machine learning method that efficiently predicts vibrational thermal properties of materials from first principles, significantly reducing computational costs while maintaining accuracy.

Contribution

The authors develop a symmetry-invariant neural network model trained on limited DFT data to accurately compute temperature-dependent electronic properties, enabling large-scale sampling.

Findings

Achieved accurate predictions of silicon's electronic energy gap at finite temperatures.

Reduced the number of required DFT calculations by an order of magnitude.

Demonstrated the effectiveness of ML in finite-temperature electronic structure calculations.

Abstract

We present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the non-perturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming {\em ab initio} calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.