Supplemental Material

The numerical results for comparison of energy and atomic forces predicted by DP model with the reference DFT results (Fig. S1), comparison of structural and dynamics properties of bulk water calculated from DPMD and AIMD simulations(Fig. S2 and Fig. S3), size dependence of the density distribution in DPMD simulations.(Fig. S4), charge distribution profiles with the water surface determined using an instantaneous interface definition (Fig. S5) and comparison of the results obtained in AIMD and MLP-based MD simulations (Fig. S6).