Machine learning approach for vibronically renormalized electronic band structures
This work addresses the efficiency problem for researchers in computational materials science by providing an incremental improvement in finite temperature first-principles electronic structure methods.
The authors tackled the computational cost of calculating vibrational thermal expectation values from first principles by developing a machine learning method that uses a deep-learning neural network to predict physical properties from phonon configurations, achieving an order of magnitude increase in sampling efficiency with less than a hundred DFT calculations for silicon's temperature-dependent electronic energy gap.
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.