Accelerating GW calculations through machine-learned dielectric matrices

The GW approach produces highly accurate quasiparticle energies, but its application to large systems is computationally challenging due to the difficulty in computing the inverse dielectric matrix. To address this challenge, we develop a machine learning approach to efficiently predict density-density response functions (DDRF) in materials. An atomic decomposition of the DDRF is introduced, as well as the neighborhood density-matrix descriptor, both of which transform in the same way under rotations. The resulting DDRFs are then used to evaluate quasiparticle energies via the GW approach. To assess the accuracy of this method, we apply it to hydrogenated silicon clusters and find that it reliably reproduces HOMO-LUMO gaps and quasiparticle energy levels. The accuracy of the predictions deteriorates when the approach is applied to larger clusters than those in the training set. These advances pave the way for GW calculations of complex systems, such as disordered materials, liquids, interfaces, and nanoparticles.