Efficient ensemble averaging methods to study electronic structure at finite temperature from first principles calculations using neural network*

Calculating electronic and lattice properties of materials at finite temperature in the presence of disorder and defects is important for data-driven design and discovery of materials. One of the current methods for calculating temperature dependent electronic structure of materials, within first principles calculations, is the use of perturbative Feynman diagram method which involves calculation of electron-phonon matrix elements and electronic self-energy corrections. An alternative non-perturbative approach which avoids the calculation of the electron-phonon matrix elements altogether is to perform configurational averaging over many nuclear supercell configurations. While easy to implement in first-principles code and possibly advantageous to explore effects beyond the harmonic regime, these methods require sampling over many extremely large supercells to get accurate results. In this work, we propose a rigorous group theory-based supervised machine learning (ML) method which can reduce the computational cost of such finite temperature calculations. We demonstrate that our Density functional theory+ML based approach, after appropriate training and neural network optimization, can i) reduce the number of DFT calculations necessary to perform ensemble average for a given temperature and ii) efficiently predict the temperature dependence of electronic band gap thereby making finite temperature electronic structure calculations computationally tractable.