  We show how machine learning techniques based on Bayesian inference can be
used to reach new levels of realism in the computer simulation of molecular
materials, focusing here on water. We train our machine-learning algorithm
using accurate, correlated quantum chemistry, and predict energies and forces
in molecular aggregates ranging from clusters to solid and liquid phases. The
widely used electronic-structure methods based on density-functional theory
(DFT) give poor accuracy for molecular materials like water, and we show how
our techniques can be used to generate systematically improvable corrections to
DFT. The resulting corrected DFT scheme gives remarkably accurate predictions
for the relative energies of small water clusters and of different ice
structures, and greatly improves the description of the structure and dynamics
of liquid water.
