Our methodology closely follows our previous work , where we have constructed machine-learning potentials (MLPs) for water for one semi-local density functional. The adopted strategy uses rst on-the-y training following the isobars using NPT simulations. Simulations cover ice, melting of ice and water in a temperature range between the supercooled state to slightly below the evaporation point. Further structures are added from parallel-tempering simulations along the isobar of water. The nal dataset consists of about 1500 structures with typically 64 molecules. To obtain a highly accurate database, we have opted to use the hardest and most accurate potentials available for VASP (O h and H h). For the present work, we exclusively use the MLP implementation available in VASP. The on-the-y training relies on Gaussian process regression using Bayesian regression . However, for the production runs we rely on kernel-ridge regression .