  The GW approach produces highly accurate quasiparticle energies, but its
application to large systems is computationally challenging, which can be
largely attributed 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. For
this, an atomic decomposition of the DDRF is introduced as well as the
neighbourhood 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. This technique is called the ML-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 included in the training set. These
advances pave the way towards GW calculations of complex systems, such as
disordered materials, liquids, interfaces and nanoparticles.
