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Extending atomic decomposition and many-body representation with a chemistry-motivated approach to machine learning potentials

Nature Computational Science volume 5, pages 418–426 (2025)Cite this article

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Abstract

Most widely used machine learning potentials for condensed-phase applications rely on many-body permutationally invariant polynomial or atom-centered neural networks. However, these approaches face challenges in achieving chemical interpretability in atomistic energy decomposition and fully matching the computational efficiency of traditional force fields. Here we present a method that combines aspects of both approaches and balances accuracy and force-field-level speed. This method utilizes a monomer-centered representation, where the potential energy is decomposed into the sum of chemically meaningful monomeric energies. The structural descriptors of monomers are described by one-body and two-body effective interactions, enforced by appropriate sets of permutationally invariant polynomials as inputs to the feed-forward neural networks. Systematic assessments of models for gas-phase water trimer, liquid water, methane–water cluster and liquid carbon dioxide are performed. The improved accuracy, efficiency and flexibility of this method have promise for constructing accurate machine learning potentials and enabling large-scale quantum and classical simulations for complex molecular systems.

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Fig. 1: Schematic of the MB-PIPNet architecture.
Fig. 2: Potential energy predictions and MD simulation results of liquid water by MB-PIPNet model.
Fig. 3: Computational cost of MB-PIPNet model.

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Data availability

All data generated or analyzed during this study are available at https://doi.org/10.6084/m9.figshare.28510238.v1 (ref. 65). Source data are provided with this paper.

Code availability

The source codes and examples of the MB-PIPNet approach are available on Zenodo at https://doi.org/10.5281/zenodo.14954863 (ref. 66) and GitHub at (https://github.com/qiyuchem/MB-PIPNet and https://github.com/szquchen/MSA-2.0).

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Acknowledgements

Q.Y. and D.H.Z. acknowledge the support from National Natural Science Foundation of China (grant numbers 22473030 and 22288201). J.M.B. acknowledges support from NASA grant (80NSSC22K1167). R.C. thanks Università degli Studi di Milano for financial support under grant PSR2022_DIP_005_PI_RCONT.

Author information

Authors and Affiliations

  1. Department of Chemistry, Fudan University, Shanghai, China

    Qi Yu & Ruitao Ma

  2. Shanghai Innovation Institute, Shanghai, China

    Qi Yu

  3. Independent Researcher, Toronto, Ontario, Canada

    Chen Qu

  4. Dipartimento di Chimica, Università degli Studi di Milano, Milan, Italy

    Riccardo Conte

  5. Department of Physics and Materials Science, University of Luxembourg, Luxembourg City, Luxembourg

    Apurba Nandi

  6. Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, GA, USA

    Priyanka Pandey & Joel M. Bowman

  7. Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA

    Paul L. Houston

  8. State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China

    Dong H. Zhang

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Contributions

Q.Y. conceived of the project, performed calculations and analyzed the data. R.M. performed timing tests. D.H.Z. and J.M.B. provided critical feedback. All authors discussed the results and contributed to writing the paper.

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Correspondence to Qi Yu.

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Nature Computational Science thanks Bin Jiang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team.

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Extended data

Extended Data Fig. 1 Potential energy predictions from MB-PIPNet model of water trimer.

(a) Energy-energy correlation plot for MB-PIPNet model of water trimer with reference energies calculated using q-AQUA-pol. (b) Potential energy curve predicted by MB-PIPNet model with comparison to q-AQUA-pol reference data. Atom colors: H-white, O-red.

Source data

Extended Data Fig. 2 Structural properties of liquid water at different temperatures predicted by MB-PIPNet model.

OO radial distribution function from classical molecular dynamics simulations at different temperatures using MB-PIPNet model. The MB-pol data are taken from ref. 51. The experimental data are taken from ref. 71,72.

Source data

Extended Data Fig. 3 Performance of the MB-PIPNet model for methane-water clusters and liquid CO2.

(a) Correlation plots of test datasets for gas-phase CH4(H2O)2 cluster with reference energies calculated using previously reported potential56. (b) Correlation plots of test datasets for liquid CO2 with 64 molecules in simulation box with reference energies calculated at the BLYP-D3 level of theory57.

Source data

Supplementary information

Supplementary Information (download PDF )

Supplementary Table 1, Figs. 1–5 and Sections 1–5.

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Yu, Q., Ma, R., Qu, C. et al. Extending atomic decomposition and many-body representation with a chemistry-motivated approach to machine learning potentials. Nat Comput Sci 5, 418–426 (2025). https://doi.org/10.1038/s43588-025-00790-0

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