  Kohn-Sham density functional theory (DFT) is the standard method for
first-principles calculations in computational chemistry and materials science.
More accurate theories such as the random-phase approximation (RPA) are limited
in application due to their large computational cost. Here, we construct a DFT
substitute functional for the RPA using supervised and unsupervised machine
learning (ML) techniques. Our ML-RPA model can be interpreted as a non-local
extension to the standard gradient approximation. We train an ML-RPA functional
for diamond surfaces and liquid water and show that ML-RPA can outperform the
standard gradient functionals in terms of accuracy. Our work demonstrates how
ML-RPA can extend the applicability of the RPA to larger system sizes, time
scales and chemical spaces.
