Let us begin our more detailed discussion with optPBE, a functional that introduces vdW interactions through terms dependent on the density at two distinct points in space. This departs from conventional semilocal density functionals, which typically only consider semi-local information at a single point in space. As already noted above, the isobars for the two training sets are very similar. Both simulations lack a clear density maximum. Instead, the density increases almost linearly with decreasing temperature, with an abrupt jump to a low-density amorphous ice phase around 210 K. This result is reproducible, as conrmed by the two independent MLPs and thus independent of database details. A very similar unsatisfactory result is observed for revPBE0-D3/zd. Again, there is no discernible density maximum and an abrupt transition to a sort of low-density amorphous ice structure occurs around 210 K. Both functionals, optPBE and revPBE0-D3/zd, overestimate the density dierence between water and ice, which appears to be the primary cause of the lack of a discernible density maximum. Also, their melting points occur at a very low temperature. On the other hand, the revPBE0-D3/BJ functional predicts densities that are too low, somewhat similar but slightly better than for the semi-local functionals with vdW corrections. Similar to revPBE0-D3/zd, PBE0-D3/zd yields a density that is too large but now a density maximum is discernible, albeit at a temperature that is too high, and the dierence in density between water and ice is quite close to the experimental value. For PBE0-D3/BJ, the density isobar is very similar in shape to revPBE0-D3/BJ, but shifted to higher densities and temperatures. In fact, the melting points for all functionals are, in general, signicantly too high, except for optPBE and revPBE0-D3/zd, which are too low.