The many-body expansion combined with neural networks

Yao, Kun; Herr, John E.; Parkhill, John

doi:10.1063/1.4973380

Cited by 120Advanced Chemical Physics StudiesMachine Learning in Materials ScienceComputational Drug Discovery Methods

The many-body expansion combined with neural networks

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Yao, Kun, Herr, John E., Parkhill, John·2017·The Journal of Chemical Physics

DOI 10.1063/1.4973380

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Abstract

Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of calculations required for chemical accuracy is still prohibitively expensive for the ab initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab initio potential energy surfaces have improved, especially non-linear models based on neural networks (NNs) which can reproduce ab initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN’s and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size while reducing the scaling problem of large systems. NN’s reduce, by a factor in excess of 106, the computational overhead of the MBE and reproduce the accuracy of ab initio calculations without specialized force fields. We show that for a small molecule extended system like methanol, accuracy can be achieved with drastically different chemical embeddings. To assess this we test a new chemical embedding which can be inverted to predict molecules with desired properties. We also provide our open-source code for the neural network many-body expansion, Tensormol.

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Accurate Localization of 3D Objects from RGB-D Data Using Segmentation Hypotheses
Kim, B.-S., Xu, S., & Savarese, S. (2013) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2013.409 · Cited by 60 · cited 1× · see citing works
“82 An example D-map can be seen in Figure 1.”
Background
Fitting sparse multidimensional data with low-dimensional terms
Manzhos, S., Yamashita, K., & Carrington, T. (2009) · Computer Physics Communications · doi:10.1016/j.cpc.2009.05.022 · Cited by 57 · see citing works
Effects of reagent rotational excitation on the H + CHD3 → H2 + CD3 reaction: A seven dimensional time-dependent wave packet study
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Communication: Separable potential energy surfaces from multiplicative artificial neural networks
Koch, W., & Zhang, D. H. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4887508 · Cited by 54 · see citing works
Methanol clusters (CH3OH)n: Putative global minimum-energy structures from model potentials and dispersion-corrected density functional theory
Kazachenko, S., Bulusu, S. S., & Thakkar, A. J. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4809528 · Cited by 52 · cited 1× · see citing works
“Table II gives the relative energies of the three minimal energy geometries, chair, bowl and chain 89 of a methanol trimer.”
Background
Global Potential Energy Surface for the H+CH4↔H2+CH3 Reaction using Neural Networks
Xu, X., Chen, J., & Zhang, D. H. (2014) · Chinese Journal of Chemical Physics · doi:10.1063/1674-0068/27/04/373-379 · Cited by 52 · see citing works
Vibrational Circular Dichroism Spectra for Large Molecules through Molecules-in-Molecules Fragment-Based Approach
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Building Part-Based Object Detectors via 3D Geometry
Shrivastava, A., & Gupta, A. (2013) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2013.219 · Cited by 39 · see citing works
Dimers of Dimers (DOD): A New Fragment-Based Method Applied to Large Water Clusters
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Many-Body Convergence of the Electrostatic Properties of Water
Medders, G. R., & Paesani, F. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct400696d · Cited by 36 · see citing works
Permutationally invariant fitting of intermolecular potential energy surfaces: A case study of the Ne-C2H2 system
Li, J., & Guo, H. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4936660 · Cited by 27 · see citing works
Real space electrostatics for multipoles. I. Development of methods
Lamichhane, M., Gezelter, J. D., & Newman, K. E. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4896627 · Cited by 23 · see citing works
Real space electrostatics for multipoles. II. Comparisons with the Ewald sum
Lamichhane, M., Newman, K. E., & Gezelter, J. D. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4896628 · Cited by 18 · see citing works
Reactive Many-Body Expansion for a Protonated Water Cluster
Pinski, P., & Cśanyi, G. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct400488x · Cited by 17 · cited 2× · see citing works
“3,6,9,21 .”
Background
Molecular Engineering of Torsional Potentials in Fluorogenic Dyes via Electronic Substituent Effects
Ediz, V., Lee, J. L., Armitage, B. A., & Yaron, D. (2008) · The Journal of Physical Chemistry A · doi:10.1021/jp805546s · Cited by 14 · see citing works
Computationally efficient characterization of potential energy surfaces based on fingerprint distances
Schaefer, B., & Goedecker, S. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4956461 · Cited by 11 · see citing works
Using Molecular Similarity to Develop Reliable Models of Chemical Reactions in Complex Environments
Ediz, V., Monda, A. C., Brown, R. P., & Yaron, D. (2009) · Journal of Chemical Theory and Computation · doi:10.1021/ct9004195 · Cited by 6 · see citing works

Flagged first, then by citations

1 of the 106 references couldn’t be matched to a known paper.

Research works printed but not linked: 2

83 I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. WardeFarley, S. Ozair, A. Courville, and Y. Bengio, 'Generative adversarial nets,' in Advances in Neural Information Processing Systems 27 , edited by Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger (Curran Associates, Inc., 2014) pp. 2672-2680.
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QSAR without borders
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First Principles Neural Network Potentials for Reactive Simulations of Large Molecular and Condensed Systems
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Machine learning molecular dynamics for the simulation of infrared spectra
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The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics
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Neural Network Potential Energy Surfaces for Small Molecules and Reactions
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Unified representation of molecules and crystals for machine learning
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“Following recent work connecting ML with many-body expansions [17,24], we generalize to the MBTR equation”
sGDML: Constructing accurate and data efficient molecular force fields using machine learning
Chmiela, S., Sauceda, H. E., Poltavsky, I., Müller, K., & Tkatchenko, A. (2019) · Computer Physics Communications · doi:10.1016/j.cpc.2019.02.007 · Cited by 241 · see citing works
Quantum Machine Learning in Chemical Compound Space
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Machine learning for the structure–energy–property landscapes of molecular crystals
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Predicting electronic structure properties of transition metal complexes with neural networks
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Atom-density representations for machine learning
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Deep Learning for Nonadiabatic Excited-State Dynamics
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Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions
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Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions.
Nguyen, T. T. M., Székely, E., Imbalzano, G., Behler, J., Cśanyi, G., Ceriotti, M., Götz, A. W., & Paesani, F. (2018) · Apollo (University of Cambridge) · doi:10.17863/cam.22160 · Cited by 168 · see citing works
Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization
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Intrinsic Bond Energies from a Bonds-in-Molecules Neural Network
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Self-citation
Predicting electronic structure properties of transition metal complexes with neural networks
Janet, J. P., & Kulik, H. J. (2017) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 134 · see citing works
Molecular force fields with gradient-domain machine learning: Construction and application to dynamics of small molecules with coupled cluster forces
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Molecular force fields with gradient-domain machine learning: Construction and application to dynamics of small molecules with coupled cluster forces
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Perspective: Computational chemistry software and its advancement as illustrated through three grand challenge cases for molecular science
Krylov, A. I., Windus, T. L., Barnes, T., Marin‐Rimoldi, E., Nash, J. A., Pritchard, B. P., Smith, D. G. A., Altarawy, D., Saxe, P. W., Clementi, C., et al. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5052551 · Cited by 99 · see citing works
Machine learning for quantum dynamics: deep learning of excitation energy transfer properties
Häse, F., Kreisbeck, C., & Aspuru‐Guzik, A. (2017) · Chemical Science · doi:10.1039/c7sc03542j · Cited by 92 · see citing works
Molecular representations for machine learning applications in chemistry
Raghunathan, S., & Priyakumar, U. D. (2021) · International Journal of Quantum Chemistry · doi:10.1002/qua.26870 · Cited by 102 · see citing works
A Mixed Quantum Chemistry/Machine Learning Approach for the Fast and Accurate Prediction of Biochemical Redox Potentials and Its Large-Scale Application to 315 000 Redox Reactions
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Incorporating Electronic Information into Machine Learning Potential Energy Surfaces via Approaching the Ground-State Electronic Energy as a Function of Atom-Based Electronic Populations
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Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit
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Many-Body Descriptors for Predicting Molecular Properties with Machine Learning: Analysis of Pairwise and Three-Body Interactions in Molecules
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Application of Computational Biology and Artificial Intelligence Technologies in Cancer Precision Drug Discovery
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“Many scientifically intensified problems have been explored recently such as solvation for Schrodinger equation [152], machinelearned density functional development [153–156], classification of chemical trajectory data, predictions of the molecular properties prediction of the excited state electrons [157, 158], many-…”
Background
A review of machine learning in geochemistry and cosmochemistry: Method improvements and applications
He, Y., Zhou, Y., Wen, T., Zhang, S., Huang, F., Zou, X., Ma, X., & Zhu, Y. (2022) · Applied Geochemistry · doi:10.1016/j.apgeochem.2022.105273 · Cited by 85 · see citing works
Atomic Energies from a Convolutional Neural Network
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Metadynamics for training neural network model chemistries: A competitive assessment
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“8 Diverse network types have been introduced to model energies as a sum of atoms 9–12 or as a sum of bonds, 13 a many-body expansion, 14 and even generalized hierarchical schemes.”
BackgroundSelf-citation
Heterogeneous Molecular Graph Neural Networks for Predicting Molecule Properties
Shui, Z., & Karypis, G. (2020) · Proceedings · doi:10.1109/icdm50108.2020.00058 · Cited by 76 · see citing works
“The many-body expansion (MBE) [8]–[10] is an important scheme that computes the energy of an N -particle system as the sum of the contributions of many-body terms”
Background
The Shape of Full Configuration Interaction to Come
Eriksen, J. J. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.0c03225 · Cited by 66 · see citing works
Energy-free machine learning force field for aluminum
Kruglov, I. A., Sergeev, O., Yanilkin, A. V., & Оганов, А. Р. (2017) · Scientific Reports · doi:10.1038/s41598-017-08455-3 · Cited by 67 · see citing works
Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime
Eriksen, J. J., & Gauß, J. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00680 · Cited by 61 · see citing works
Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime
Eriksen, J. J., & Gauß, J. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00456 · Cited by 59 · see citing works
Advanced models for water simulations
Demerdash, O., Wang, L., & Head-Gordon, T. L. (2017) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1355 · Cited by 58 · see citing works
“We expect that ML models will continue to make an impact in the simulation of water, perhaps in combination with physically motivated models; the combined application of many-body expansions with ANN potentials has been explored recently.(145)”
Background
Recent Progress of Artificial Intelligence Application in Polymer Materials
Long, T., Pang, Q., Deng, Y., Pang, X., Zhang, Y., Yang, R., & Zhou, C. (2025) · Polymers · doi:10.3390/polym17121667 · Cited by 62 · see citing works
“For instance, Parkhill and collaborators developed the TensorMol model, which integrates many-body expansions with NNs to account for long-range physical interactions such as Coulombic and dispersion forces, which are often neglected in standard DFT [125].”
Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields
Sauceda, H. E., Gastegger, M., Chmiela, S., Müller, K., & Tkatchenko, A. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0023005 · Cited by 49 · see citing works
Force Field for Water Based on Neural Network
Wang, H., & Yang, W. (2018) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.8b01131 · Cited by 53 · see citing works
“74 But again, this was not developed for the force field purpose.”
Background
Phase diagram of uranium fromab initiocalculations and machine learning
Kruglov, I. A., Yanilkin, A. V., Оганов, А. Р., & Korotaev, P. Y. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.174104 · Cited by 50 · see citing works
Challenges for machine learning force fields in reproducing potential energy surfaces of flexible molecules
Vassilev-Galindo, V., Fonseca, G., Poltavsky, I., & Tkatchenko, A. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0038516 · Cited by 43 · see citing works
Molecular Dynamics Simulation of Zinc Ion in Water with an ab Initio Based Neural Network Potential
Xu, M., Zhu, T., & Zhang, J. Z. H. (2019) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.9b04087 · Cited by 43 · see citing works
An On-the-Fly Approach to Construct Generalized Energy-Based Fragmentation Machine Learning Force Fields of Complex Systems
Cheng, Z., Zhao, D., Ma, J., Li, W., & Li, S. (2020) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.0c04526 · Cited by 35 · see citing works
Gaussian process model of 51-dimensional potential energy surface for protonated imidazole dimer
Sugisawa, H., Ida, T., & Krems, R. V. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0023492 · Cited by 36 · see citing works
“This previous work has demonstrated many useful ML approaches to constructing PES and force fields for a variety of systems, including models based on neural networks (NNs) [28–41, 56, 60, 65–68] and kernel methods [3, 19, 42–55, 61–64, 69–72], including GP regression [19, 42–53, 55].”
Surrogate modeling of hydrodynamic forces between multiple floating bodies through a hierarchical interaction decomposition
Zhang, J., Taflanidis, A. A., & Scruggs, J. T. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109298 · Cited by 27 · see citing works
Adaptive frozen orbital treatment for the fragment molecular orbital method combined with density-functional tight-binding
Nishimoto, Y., & Fedorov, D. G. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5012935 · Cited by 25 · see citing works
A new approach for the prediction of partition functions using machine learning techniques
Desgranges, C., & Delhommelle, J. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5037098 · Cited by 25 · see citing works
Delocalization error poisons the density-functional many-body expansion
Broderick, D. R., & Herbert, J. M. (2024) · Chemical Science · doi:10.1039/d4sc05955g · Cited by 23 · see citing works
Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration
Broderick, D. R., & Herbert, J. M. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0174293 · Cited by 23 · see citing works
Hochdimensionale neuronale Netze für Potentialhyperflächen großer molekularer und kondensierter Systeme
Behler, J. (2017) · Angewandte Chemie · doi:10.1002/ange.201703114 · Cited by 22 · see citing works
Characterizing Protein–Ligand Binding Using Atomistic Simulation and Machine Learning: Application to Drug Resistance in HIV-1 Protease
Whitfield, T. W., Ragland, D. A., Zeldovich, K. B., & Schiffer, C. A. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00781 · Cited by 24 · see citing works
Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics
Carpenter, B. K., Ezra, G. S., Farantos, S. C., Kramer, Z. C., & Wiggins, S. (2017) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.7b08707 · Cited by 22 · see citing works
Automatically Constructed Neural Network Potentials for Molecular Dynamics Simulation of Zinc Proteins
Xu, M., Zhu, T., & Zhang, J. Z. H. (2021) · Frontiers in Chemistry · doi:10.3389/fchem.2021.692200 · Cited by 19 · see citing works
“(Wang and Yang, 2018) Currently there are several open-source packages like DeepMD-kit (Wang et al., 2018), TensorMol (Yao et al., 2017; Yao et al., 2018), and TorchMD (Doerr et al., 2021) which can train neural network potentials for speci ﬁ c molecular systems in a straightforward manner.”
Method
Enhancing the Performance of Global Optimization of Platinum Cluster Structures by Transfer Learning in a Deep Neural Network
Yang, Q., Jiang, G.-D., & He, S. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00923 · Cited by 19 · see citing works
Machine learning prediction of interaction energies in rigid water clusters
Bose, S., Dhawan, D., Nandi, S., Sarkar, R. R., & Ghosh, D. (2018) · Physical Chemistry Chemical Physics · doi:10.1039/c8cp03138j · Cited by 19 · see citing works
Parametrically Managed Activation Function for Fitting a Neural Network Potential with Physical Behavior Enforced by a Low-Dimensional Potential
Akher, F. B., Shu, Y., Varga, Z., Bhaumik, S., & Truhlar, D. G. (2023) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.3c02627 · Cited by 19 · see citing works
Accurate Molecular Dynamics Enabled by Efficient Physically Constrained Machine Learning Approaches
Chmiela, S., Sauceda, H. E., Tkatchenko, A., & Müller, K.-R. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-40245-7_7 · Cited by 17 · see citing works
“As an alternative, a series of methodological advances in the field of machine learning (ML) [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55] have yielded univ…”
Background
Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning
Rogers, J., Lee, T.-H., Pakdel, S., Xu, W., Dobrosavljević, V., Yao, Y.-X., Ove Christiansen, A., & Lanatà, N. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013101 · Cited by 16 · see citing works
““n-mode representation” [46, 47] —previously used for effectively reducing the dimensionality of large-scale regression problems (e.”
Method
Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes
Vennelakanti, V., Kilic, I. B., Terrones, G., Duan, C., & Kulik, H. J. (2023) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.3c07104 · Cited by 18 · see citing works
Classification of spatially resolved molecular fingerprints for machine learning applications and development of a codebase for their implementation
Reveil, M., & Clancy, P. (2018) · Molecular Systems Design & Engineering · doi:10.1039/c8me00003d · Cited by 17 · see citing works
Wave Functions, Density Functionals, and Artificial Intelligence for Materials and Energy Research: Future Prospects and Challenges
Mosquera, M. A., Fu, B., Kohlstedt, K. L., Schatz, G. C., & Ratner, M. A. (2017) · ACS Energy Letters · doi:10.1021/acsenergylett.7b01058 · Cited by 16 · see citing works
Building Nonparametric n-Body Force Fields Using Gaussian Process Regression
Glielmo, A., Zeni, C., Fekete, Á., & Vita, A. D. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-40245-7_5 · Cited by 16 · see citing works
The many-body expansion for metals. I. The alkaline earth metals Be, Mg, and Ca
Mato, J., Tzeli, D., & Xantheas, S. S. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0094598 · Cited by 15 · see citing works
Modeling molecular ensembles with gradient-domain machine learning force fields
Maldonado, A. M., Poltavsky, I., Vassilev-Galindo, V., Tkatchenko, A., & Keith, J. A. (2023) · Digital Discovery · doi:10.1039/d3dd00011g · Cited by 15 · see citing works
Massively parallelization strategy for material simulation using high‐dimensional neural network potential
Shang, C., Huang, S., & Liu, Z. (2018) · Journal of Computational Chemistry · doi:10.1002/jcc.25636 · Cited by 14 · see citing works
Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights
Sauceda, H. E., Chmiela, S., Poltavsky, I., Müller, K.-R., & Tkatchenko, A. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-40245-7_14 · Cited by 18 · see citing works
Physics-constrained Gaussian process model for prediction of hydrodynamic interactions between wave energy converters in an array
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Self-citation
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Integrating Graph Neural Networks and Many-Body Expansion Theory for Potential Energy SurfacesPreprint
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Development of generalized potential-energy surfaces using many-body expansions, neural networks, and moiety energy approximations
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Authors: Yao, K., Herr, J. E., & Parkhill, J.
Affiliations: University of Notre Dame (US)
ORCID: Yao, Kun
Herr, John E.
Parkhill, John
Venue: The Journal of Chemical Physics
Publisher: AIP Publishing
Published: 2017-01-04
Volume: 146
Issue: 1
Pages: 014106-014106
ISSN: 0021-9606 (ISSN-L)
1089-7690
DOI: 10.1063/1.4973380
OpenAlex: W2526734845
Cited by: 120
References: 106
Citations by year: 2026: 4 · 2025: 10 · 2024: 4 · 2023: 11 · 2022: 10 · 2021: 6 · 2020: 18 · 2019: 16 · 2018: 25 · 2017: 16
FWCI: 10.06
Type: journal article
Language: en
Open access: green
arxiv.org
Locations: The Journal of Chemical Physics (publishedVersion)
PubMed (publishedVersion)
arXiv (Cornell University) (submittedVersion)
arXiv (Cornell University)
Funders: UND chemistry dept startup funds
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
Keywords: many-body expansion, artificial neural networks, ab initio potential energy surface, fragmentation methods, large-scale quantum chemistry, computational scaling, methanol, molecular property prediction

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