Meta-optimization of maximally-localized Wannier functions

TL;DR

This paper presents a universal meta-optimization method using machine learning to automate and accelerate the generation of maximally-localized Wannier functions, enhancing their application in materials science.

Contribution

The authors introduce a novel, automated meta-optimization approach that significantly improves the efficiency and accuracy of Wannier function generation in complex electronic systems.

Findings

Autonomous interpolation of entangled band structures with millielectronvolt accuracy.

Thousand-fold acceleration of Boltzmann transport calculations.

Ultra-fast high-throughput Wannier function computations for large materials datasets.

Abstract

Maximally-localized Wannier functions are quantum wavefunctions resembling atomic orbitals that are used to describe electrons in condensed matter. Since their introduction in 1997, these functions have become ubiquitous in ab initio materials simulations, including applications in linear-scaling methods, strongly-correlated electron systems, quantum transport, electron-phonon interactions, and topological materials. Despite their widespread adoption in a vast software ecosystem, Wannier functions have not yet attained their fullest potential in the presence of entangled bands, as their optimization remains challenging and labor-intensive. Here, we introduce a universal meta-optimization method that leverages workflow abstraction and machine learning techniques like differential evolution and Bayesian optimization to generate globally optimized Wannier functions without human intervention. We demonstrate this approach through three applications: (i) autonomous interpolation of entangled band structures with millielectronvolt accuracy starting from coarse Brillouin zone grids, (ii) thousand-fold acceleration of fully ab initio Boltzmann transport calculations via the use of minimal coarse Brillouin zone grids, and (iii) ultra-fast high-throughput calculations of high-precision Wannier functions for large materials libraries. This work brings calculations that previously required supercomputers within the reach of personal computers.