  Machine learning models are rapidly becoming widely used to simulate complex
physicochemical phenomena with ab initio accuracy. Here, we use one such model
as well as direct density functional theory (DFT) calculations to investigate
the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an
eye towards studying ice nucleation. The machine learning model is based on
deep neural networks and has been trained on DFT data obtained using the SCAN
exchange and correlation functional. We use this model to drive enhanced
sampling simulations aimed at calculating a number of complex properties that
are out of reach of DFT-driven simulations and then employ an appropriate
reweighting procedure to compute the corresponding properties for the SCAN
functional. This approach allows us to calculate the melting temperature of
both ice polymorphs, the driving force for nucleation, the heat of fusion, the
densities at the melting temperature, the relative stability of ice Ih and Ic,
and other properties. We find a correct qualitative prediction of all
properties of interest. In some cases, quantitative agreement with experiment
is better than for state-of-the-art semiempirical potentials for water. Our
results also show that SCAN correctly predicts that ice Ih is more stable than
ice Ic.
