Paesani Research Group

Laboratory for Theoretical and Computational Chemistry at UC San Diego  


© Paesani Research Group. All rights reserved.

DNN@MB-pol is a deep neural network potential trained on MB-pol data that we developed in Ref. [1] using the smooth edition of the deep potential (DeepPot-SE) toolkit [2] following the procedure reported in Ref. [3]. All details related to the development of DNN@MB-pol are reported in the Supplementary Information of Ref. [1].

Briefly, we used 25, 50, and 100 neurons for the hidden embedding layers, respectively, while the submatrix of the embedding matrix uses 16 neurons. The distance cutoff was set to 6 Å with a smooth cutoff region of 0.5 Å. The DNN@MB-pol potential is represented by a fully connected deep neural network with three layers of 240 neurons each. The training set for DNN@MB-pol was constructed from that of the DNN potential introduced in Ref. [4], which includes configurations collected from MB-pol simulations of water carried out between 188 K and 368 K at 1 atm [5], as well as configurations selected through active learning iterations that allow the DNN potential to accurately reproduce various thermodynamic properties of liquid water calculated with MB-pol at 1 atm. To guarantee full transferability of the DNN@MB-pol potential over a wider range of thermodynamic conditions, the original DNN training set was expanded by including configurations of supercooled water at high pressure, as well as configurations of 18 ice phases spanning a comprehensive set of thermodynamic conditions. The complete training set of DNN@MB-pol is deposited on Zenodo.

MB-pol reference energies and forces for all training set configurations were calculated using the MBX software.

The DNN@MB-pol potential was trained for 4 million steps using the DeePMD-kit [2], with a learning rate starting at 0.0005 and decreasing linearly every 5000 steps to 1.8×10−8. The initial weighting factor for the energy was set to 0.2 and increased linearly to 1.0 during the training process. The initial weighting factor for the forces was set to 1000 and decreased linearly to 1.0 at during the training process. The learning curves reported in Ref. [1] demonstrate that both energies and forces of the DNN@MB-pol potential reach well-behaved convergence at the end of the training process. Importantly, training and validation sets exhibit similar root-mean-square errors (RMSEs), which indicates that the DNN@MB-pol potential is not in the overfitting regime at any stage of the training process. The RMSE associated with the DNN@MB-pol forces plateaus at approximately 0.4 kJ mol−1A−1, which is of similar magnitude to RMSEs reported for other state-of-the-art machine-learned potentials.

The DNN@MB-pol potential can be downloaded from our repository and can be used to perform molecular dynamics with LAMMPS patched with the DeePMD-kit [3]. We recommend using the compressed version (graph-compress.pb) of the DNN@MB-pol potential, which efffectively provides the same accuracy as the uncompressed network but offers better performance [6].  


1)   S.L. Bore, F. Paesani, Realistic phase diagram of water from “first principles” data-driven quantum simulations, Nat.

      Commmun. 14, 3349 (2023).

2)   L. Zhang, J. Han, H. Wang, W. Saidi, R. Car, End-to-end symmetry preserving inter-atomic potential energy model for

      finite and extended systems, Adv. Neural Inf. Process Syst. 31 (2018).

3)   H. Wang, L. Zhang, J. Han, W. E, DeePMD-kit: A deep learning package for many-body potential energy

       representation and molecular dynamics, Comput. Phys. Commun. 228, 178 (2018).

4)   Y. Zhai, A. Caruso, S.L. Bore, Z. Luo, F. Paesani, A "short blanket" dilemma for a state-of-the-art neural network

      potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

      J. Chem. Phys. 158, 084111 (2023).

5)  T.E. Gartner III, K.M. Hunter, E. Lambros, A. Caruso, M. Riera, G.R. Medders, A.Z. Panagiotopoulos,

      P.G. Debenedetti, F. Paesani, Anomalies and local structure of liquid water from boiling to the supercooled

      regime as predicted by the many-body MB-pol model, J. Phys. Chem. Lett. 13, 3652 (2022).

6)   D. Lu, W. Jiang, Y. Chen, L. Zhang, W. Jia, H. Wang, M. Chen, DP compress: A model compression scheme for

      generating efficient deep potential models, J. Chem. Theory Comput. 18, 5559 (2022).