Meta-optimization of maximally-localized Wannier functions

Abstract Maximally-localized Wannier functions are quantum wavefunctions resembling atomic orbitals that are used to describe electrons in condensed matter 1 . Since their introduction in 1997 2 , these functions have become ubiquitous in ab initio materials simulations, including applications in linear-scaling methods 3 , strongly correlated electron systems 4 , quantum transport 5 , electron-phonon interactions 6 , and topological materials 7 . Despite their widespread adoption in a vast software ecosystem 8 , 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) ultrafast 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.