Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations
Abstract
The accuracy of the results obtained in molecular dynamics or Monte Carlo simulations crucially depends on a reliable description of the atomic interactions. A large variety of efficient potentials has been proposed in the literature, but often the optimum functional form is difficult to find and strongly depends on the particular system. In recent years, artificial neural networks (NN) have become a promising new method to construct potentials for a wide range of systems. They offer a number of advantages: they are very general and applicable to systems as different as small molecules, semiconductors and metals; they are numerically very accurate and fast to evaluate; and they can be constructed using any electronic structure method. Significant progress has been made in recent years and a number of successful applications demonstrate the capabilities of neural network potentials. In this Perspective, the current status of NN potentials is reviewed, and their advantages and limitations are discussed.
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General-purpose and systematically-convergent descriptions of chemical environments provide a starting point that is considerably less biased than descriptors based on complicated heuristics that are designed from the outset to identify e.g. a stacking order, or the coordination of a site.
“General-purpose and systematically-convergent descriptions of chemical environments, such as those that are typically used to fit potentials or predict molecular properties 31,35 , provide a starting point that is considerably less biased than descriptors based on complicated heuristics that are designed from the outset to identify e.g. a stacking order, or the coordination of a site.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [35]
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Modeling the Crystallization Kinetic Rates of Lactose via Artificial Neural Network
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Neural network‐based modeling for semi‐batch and nonisothermal free radical polymerization
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Pair potentials from diffraction data on liquids: A neural network solution
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Quantum neural networks can predict binding free energies for enzymatic inhibitors
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Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945 · see citing works
ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost
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Perspective: Machine learning potentials for atomistic simulations
Behler, J. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4966192 · Cited by 1,435 · see citing works
Self-citationQuantum-chemical insights from deep tensor neural networks
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Machine learning of accurate energy-conserving molecular force fields
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Machine Learning Interatomic Potentials as Emerging Tools for Materials Science
Deringer, V. L., Caro, M. A., & Cśanyi, G. (2019) · Advanced Materials · doi:10.1002/adma.201902765 · Cited by 1,051 · see citing works
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems
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“…Hansen et al. [120] find that parameterizations of atomic energy using ML take seconds compared to multiple days for more standard quantum-calculation calculations, and Behler et al. [27] find that neural networks can vastly improve the efficiency of finding potential energy surfaces of molecules.”
MethodPerformance and Cost Assessment of Machine Learning Interatomic Potentials
Zuo, Y., Chen, C., Li, X., Deng, Z., Chen, Y., Behler, J., Cśanyi, G., Shapeev, A. V., Thompson, A. P., Wood, M. A., et al. (2020) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.9b08723 · Cited by 919 · see citing works
Self-citationFour Generations of High-Dimensional Neural Network Potentials
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Self-citationConstructing high‐dimensional neural network potentials: A tutorial review
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Self-citationCombining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems
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Structure prediction drives materials discovery
Оганов, А. Р., Pickard, C. J., Zhu, Q., & Needs, R. J. (2019) · Nature Reviews Materials · doi:10.1038/s41578-019-0101-8 · Cited by 703 · see citing works
Behler, J. (2017) · Angewandte Chemie International Edition · doi:10.1002/anie.201703114 · Cited by 695 · see citing works
Self-citationActive learning of linearly parametrized interatomic potentials
Podryabinkin, E. V., & Shapeev, A. V. (2017) · Computational Materials Science · doi:10.1016/j.commatsci.2017.08.031 · Cited by 673 · see citing works
“Application of machine learning (ML) has recently been put forward as a promising idea that would combine the accuracy of the QM models and the e ffi ciency of the interatomic potentials [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18].”
BackgroundMachine learning based interatomic potential for amorphous carbon
Deringer, V. L., & Cśanyi, G. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.094203 · Cited by 665 · see citing works
<scp>G</scp>aussian approximation potentials: A brief tutorial introduction
Bartók, A. P., & Csányi, G. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24927 · Cited by 617 · see citing works
Assessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies
Hansen, K., Montavon, G., Biegler, F., Fazli, S., Rupp, M., Scheffler, M., von Lilienfeld, O. A., Tkatchenko, A., & Müller, K. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct400195d · Cited by 615 · see citing works
Mater, A. C., & Coote, M. L. (2019) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.9b00266 · Cited by 565 · see citing works
Machine-learned potentials for next-generation matter simulations
Friederich, P., Häse, F., Proppe, J., & Aspuru‐Guzik, A. (2021) · Nature Materials · doi:10.1038/s41563-020-0777-6 · Cited by 558 · see citing works
Robust Atomistic Modeling of Materials, Organometallic, and Biochemical Systems
Spicher, S., & Grimme, S. (2020) · Angewandte Chemie International Edition · doi:10.1002/anie.202004239 · Cited by 545 · see citing works
Permutation invariant polynomial neural network approach to fitting potential energy surfaces
Jiang, B., & Guo, H. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4817187 · Cited by 542 · see citing works
Physics-Inspired Structural Representations for Molecules and Materials
Musil, F., Grisafi, A., Bartók, A. P., Ortner, C., Cśanyi, G., & Ceriotti, M. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00021 · Cited by 556 · see citing works
Machine Learning Force Fields: Construction, Validation, and Outlook
Botu, V., Batra, R., Chapman, J., & Ramprasad, R. (2016) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.6b10908 · Cited by 516 · see citing works
“Deep learning neural networks 30 and nonlinear regression processes 13 have been the methods of choice for models describing atomic interactions.”
MethodHamiltonian Neural NetworksPreprint
Greydanus, S., Dzamba, M., & Yosinski, J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.01563 · Cited by 546 · see citing works
“Physicists, particularly those studying molecular dynamics, have seen success using neural networks to model energy surfaces [3, 11, 36, 44].”
BackgroundMachine learning molecular dynamics for the simulation of infrared spectra
Gastegger, M., Behler, J., & Marquetand, P. (2017) · Chemical Science · doi:10.1039/c7sc02267k · Cited by 556 · see citing works
Self-citationArtrith, N., & Urban, A. (2016) · Computational Materials Science · doi:10.1016/j.commatsci.2015.11.047 · Cited by 503 · see citing works
Ko, T. W., Finkler, J. A., Goedecker, S., & Behler, J. (2021) · Nature Communications · doi:10.1038/s41467-020-20427-2 · Cited by 509 · see citing works
Self-citationThe TensorMol-0.1 model chemistry: a neural network augmented with long-range physics
Yao, K., Herr, J. E., Toth, D. W., Mckintyre, R., & Parkhill, J. (2018) · Chemical Science · doi:10.1039/c7sc04934j · Cited by 475 · see citing works
On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events
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Physics-Inspired Structural Representations for Molecules and Materials
Musil, F., Grisafi, A., Bartók, A., Ortner, C., Cśanyi, G., Ceriotti, M., et al. (2021) · Cambridge University Engineering Department Publications Database · Cited by 440 · see citing works
Quantum Chemistry in the Age of Machine Learning
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Machine learning for high-entropy alloys: Progress, challenges and opportunities
Liu, X., Zhang, J., & Pei, Z. (2022) · Progress in Materials Science · doi:10.1016/j.pmatsci.2022.101018 · Cited by 417 · see citing works
“Another strategy is to estimate the prediction error with multiple models and add new data when the prediction error is larger than a threshold value, which is demonstrated for neural networks [125, 126, 127] and Gaussian process [128, 129].”
BackgroundJiang, B., Li, J., & Guo, H. (2016) · International Reviews in Physical Chemistry · doi:10.1080/0144235x.2016.1200347 · Cited by 401 · see citing works
Machine-Learning Interatomic Potentials for Materials Science
Mishin, Y. M. (2021) · Acta Materialia · doi:10.1016/j.actamat.2021.116980 · Cited by 402 · see citing works
“The reader is referred to Behler’s paper [110] for an excellent exposition of the NN method, including the exact count of the total number of parameters and comparison of different transfer functions.”
MethodAdaptive machine learning framework to accelerate ab initio molecular dynamics
Botu, V., & Ramprasad, R. (2014) · International Journal of Quantum Chemistry · doi:10.1002/qua.24836 · Cited by 388 · see citing works
Representing potential energy surfaces by high-dimensional neural network potentials
Behler, J. (2014) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/26/18/183001 · Cited by 390 · see citing works
Self-citationMachine learning for quantum mechanics in a nutshell
Rupp, M. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24954 · Cited by 358 · see citing works
Accelerating high-throughput searches for new alloys with active learning of interatomic potentials
Gubaev, K., Podryabinkin, E. V., Hart, G. L. W., & Shapeev, A. V. (2018) · Computational Materials Science · doi:10.1016/j.commatsci.2018.09.031 · Cited by 354 · see citing works
Machine Learning for Computational Heterogeneous Catalysis
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Physically informed artificial neural networks for atomistic modeling of materials
Pun, G. P. P., Batra, R., Ramprasad, R., & Mishin, Y. M. (2019) · Nature Communications · doi:10.1038/s41467-019-10343-5 · Cited by 368 · see citing works
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BackgroundMethodInfluentialNeural Network Potential Energy Surfaces for Small Molecules and Reactions
Manzhos, S., & Carrington, T. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00665 · Cited by 315 · see citing works
Imbalzano, G., Anelli, A., Giofré, D., Klees, S., Behler, J., & Ceriotti, M. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5024611 · Cited by 330 · see citing works
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Self-citationHigh-dimensional neural network potentials for metal surfaces: A prototype study for copper
Artrith, N., & Behler, J. (2012) · Physical Review B · doi:10.1103/physrevb.85.045439 · Cited by 325 · see citing works
Self-citationLi, J., Jiang, B., & Guo, H. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4832697 · Cited by 324 · see citing works
Green, M. L., Choi, C. L., Hattrick-Simpers, J. R., Joshi, A. M., Takeuchi, I., Barron, S. C., Campo, E. M., Chiang, T. P., Empedocles, S. A., Gregoire, J. M., et al. (2017) · Applied Physics Reviews · doi:10.1063/1.4977487 · Cited by 311 · see citing works
Neural Network Potentials: A Concise Overview of Methods
Kocer, E., Ko, T. W., & Behler, J. (2022) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-082720-034254 · Cited by 315 · see citing works
Self-citationLibrary-Based LAMMPS Implementation of High-Dimensional Neural Network Potentials
Singraber, A., Behler, J., & Dellago, C. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00770 · Cited by 305 · see citing works
Self-citationwACSF—Weighted atom-centered symmetry functions as descriptors in machine learning potentials
Gastegger, M., Schwiedrzik, L., Bittermann, M. R., Berzsenyi, F., & Marquetand, P. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5019667 · Cited by 297 · see citing works
Machine Learning in Materials Science
Mueller, T., Kusne, A. G., & Ramprasad, R. (2016) · Reviews in computational chemistry · doi:10.1002/9781119148739.ch4 · Cited by 311 · see citing works
A roadmap for electronic grade 2D materials
Briggs, N. C., Subramanian, S., Lin, Z., Li, X.-F., Zhang, X.-T., Zhang, K., Xiao, K., Geohegan, D., Wallace, R., Chen, L.-Q., et al. (2019) · 2D Materials · doi:10.1088/2053-1583/aaf836 · Cited by 253 · see citing works
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BackgroundMethodIntegrating Physics-Based Modeling with Machine Learning: A Survey
Willard, J., Jia, X., Xu, S., Steinbach, M. S., & Kumar, V. (2020) · Cited by 305 · see citing works
An accurate and transferable machine learning potential for carbon
Rowe, P., Deringer, V. L., Gasparotto, P., Cśanyi, G., & Michaelides, A. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0005084 · Cited by 291 · see citing works
“the development of interatomic potentials an increasingly popular approach [42, 47–50].”
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Cements in the 21 st century: Challenges, perspectives, and opportunities
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Unified representation of molecules and crystals for machine learning
Huo, H., & Rupp, M. (2022) · Machine Learning Science and Technology · doi:10.1088/2632-2153/aca005 · Cited by 392 · see citing works
“[3,46] This requires representing local chemical environments [11], which MBTR should accommodate with appropriate modifications.”
BackgroundPhysically informed artificial neural networks for atomistic modeling of materials
Pun, G. P. P., Batra, R., Ramprasad, R., & Mishin, Y. M. (2019) · RePEc: Research Papers in Economics · Cited by 278 · see citing works
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Neural network interatomic potential for the phase change material GeTe
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Self-citationCommunication: Fitting potential energy surfaces with fundamental invariant neural network
Shao, K., Chen, J., Zhao, Z., & Zhang, D. H. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4961454 · Cited by 260 · see citing works
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Extracting Knowledge from Data through Catalysis Informatics
Medford, A. J., Kunz, M. R., Ewing, S. M., Borders, T. L., & Fushimi, R. (2018) · ACS Catalysis · doi:10.1021/acscatal.8b01708 · Cited by 244 · see citing works
An accurate and transferable machine learning potential for carbon.
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Application of Artificial Neural Networks for Catalysis: A Review
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Extending the accuracy of the SNAP interatomic potential form
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Self-citationCommittee neural network potentials control generalization errors and enable active learning
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Machine learning potentials for extended systems: a perspective
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Self-citationLearning scheme to predict atomic forces and accelerate materials simulations
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Self-citationBeyond Ordered Materials: Understanding Catalytic Sites on Amorphous Solids
Goldsmith, B. R., Peters, B., Johnson, J. K., Gates, B. C., & Scott, S. L. (2017) · ACS Catalysis · doi:10.1021/acscatal.7b01767 · Cited by 194 · see citing works
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Self-citationNeural networks for local structure detection in polymorphic systems
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- Authors
- Behler, J.
- Affiliations
- Ruhr University Bochum (DE)
- Corresponding author
- Behler, Jörg
- ORCID
- Behler, Jörg
- Venue
- Physical Chemistry Chemical Physics
- Publisher
- Royal Society of Chemistry (RSC)
- Published
- 2011
- Volume
- 13
- Issue
- 40
- Pages
- 17930
- ISSN
- 1463-9076 (ISSN-L)
- 1463-9084
- OpenAlex
- W2058370262
- Cited by
- 781
- References
- 151
- Citations by year
- 2026: 27 · 2025: 58 · 2024: 54 · 2023: 71 · 2022: 68 · 2021: 79 · 2020: 89 · 2019: 66 · 2018: 58 · 2017: 88 · 2016: 33 · 2015: 28 · 2014: 27 · 2013: 23 · 2012: 11
- FWCI
- 0.93
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Chemistry Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- neural network potentials, interatomic potentials, potential energy surface, molecular dynamics, Monte Carlo simulation, interatomic interactions, electronic structure methods, large-scale simulation, machine learning for materials
- MeSH terms
- Computer Simulation, Metals, Models, Molecular, Neural Networks, Computer, Small Molecule Libraries
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