DOI: 10.1063/1.4966192. Perspective: Machine learning potentials for atomistic simulations

Perspective: Machine learning potentials for atomistic simulations

10.1063/1.4966192

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Nowadays, computer simulations have become a standard tool in essentially all fields of chemistry, condensed matter physics, and materials science. In order to keep up with state-of-the-art experiments and the ever growing complexity of the investigated problems, there is a constantly increasing need for simulations of more realistic, i.e., larger, model systems with improved accuracy. In many cases, the availability of sufficiently efficient interatomic potentials providing reliable energies and forces has become a serious bottleneck for performing these simulations. To address this problem, currently a paradigm change is taking place in the development of interatomic potentials. Since the early days of computer simulations simplified potentials have been derived using physical approximations whenever the direct application of electronic structure methods has been too demanding. Recent advances in machine learning (ML) now offer an alternative approach for the representation of potential-energy surfaces by fitting large data sets from electronic structure calculations. In this perspective, the central ideas underlying these ML potentials, solved problems and remaining challenges are reviewed along with a discussion of their current applicability and limitations.

Bibliography

Behler, J. (2016). Perspective: Machine learning potentials for atomistic simulations. The Journal of Chemical Physics, 145(17).

Authors 1

Jörg Behler (first)

References 73 Referenced 1,070

{'volume-title': 'Machine Learning', 'year': '1997', 'key': '2024052420505624800_c1'} / Machine Learning (1997)
10.1146/annurev.pc.45.100194.002255 / Annu. Rev. Phys. Chem. (1994)
10.1002/anie.199305031 / Angew. Chem. Int. Ed. (1993)
10.1016/0022-2364(89)90021-8 / J. Magn. Reson. (1989)
10.1002/jcc.10361 / J. Comput. Chem. (2004)
10.1021/ci0203702 / J. Chem. Inf. Comput. Sci. (2002)
{'edition': '3rd ed.', 'volume-title': 'Neural Networks and Learning Machines', 'year': '2008', 'key': '2024052420505624800_c7'} / Neural Networks and Learning Machines (2008)
{'volume-title': 'Gaussian Processes for Machine Learning', 'year': '2006', 'key': '2024052420505624800_c8'} / Gaussian Processes for Machine Learning (2006)
{'volume-title': 'An Introduction to Support Vector Machines and Other Kernel-based Learning Methods', 'year': '2000', 'key': '2024052420505624800_c9'} / An Introduction to Support Vector Machines and Other Kernel-based Learning Methods (2000)
10.1016/j.cossms.2016.07.002 / Curr. Opin. Solid State Mater. Sci. / Atomistic calculations and materials informatics: A review
10.1557/jmr.2016.80 / J. Mater. Res. (2016)
10.1038/srep02810 / Sci. Rep. (2013)
10.1107/S0108768102003890 / Acta Crystallogr. (2002)
10.1016/0003-9861(78)90204-7 / Arch. Biochem. Biophys. (1978)
10.1002/andp.19273892002 / Ann. Phys. (1927)
{'volume-title': 'Ab initio Molecular Dynamics: Basic Theory and Advanced Methods', 'year': '2009', 'key': '2024052420505624800_c16'} / Ab initio Molecular Dynamics: Basic Theory and Advanced Methods (2009)
{'edition': '3rd ed.', 'volume-title': 'Numerical Recipes: The Art of Scientific Programming', 'year': '2007', 'key': '2024052420505624800_c17'} / Numerical Recipes: The Art of Scientific Programming (2007)
{'volume-title': 'Curve and Surface Fitting: An Introduction', 'year': '1986', 'key': '2024052420505624800_c18'} / Curve and Surface Fitting: An Introduction (1986)
10.1016/S0009-2614(99)00881-7 / Chem. Phys. Lett. (1999)
10.1080/01442350903234923 / Int. Rev. Phys. Chem. (2009)
10.1103/PhysRevB.87.184115 / Phys. Rev. B (2013)
10.1103/PhysRevLett.114.105503 / Phys. Rev. Lett. (2015)
{'volume-title': 'Topological Indices and Related Descriptors in QSAR and QSPR', 'year': '1999', 'author': 'Deviller', 'key': '2024052420505624800_c23'} / Topological Indices and Related Descriptors in QSAR and QSPR by Deviller (1999)
10.1107/s0108767310026395 / Acta Crystallogr., Sect. A: Found. Crystallogr. (2010)
10.1007/3-540-35273-2_9 / Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1
10.1063/1.469597 / J. Chem. Phys. (1995)
10.1021/jp972209d / J. Phys. Chem. A (1998)
10.1016/j.cplett.2004.07.076 / Chem. Phys. Lett. (2004)
10.1063/1.2746232 / J. Chem. Phys. (2007)
{'key': '2024052420505624800_c30'}
{'key': '2024052420505624800_c31'}
10.1103/PhysRevLett.98.146401 / Phys. Rev. Lett. (2007)
10.1103/PhysRevLett.76.3168 / Phys. Rev. Lett. (1996)
10.1103/PhysRevB.39.5566 / Phys. Rev. B (1989)
10.1088/0953-8984/26/18/183001 / J. Phys.: Condens. Matter (2014)
10.1063/1.3553717 / J. Chem. Phys. (2011)
10.1063/1.4712397 / J. Chem. Phys. (2012)
10.1103/PhysRevLett.104.136403 / Phys. Rev. Lett. (2010)
{'key': '2024052420505624800_c39'}
10.1103/PhysRevLett.108.058301 / Phys. Rev. Lett. (2012)
10.1021/acscatal.5b02666 / ACS Catal. (2016)
10.1021/acs.jpclett.5b00831 / J. Phys. Chem. Lett. (2015)
10.1021/jp9105585 / J. Phys. Chem. A (2010)
10.1039/c1cp21668f / Phys. Chem. Chem. Phys. (2011)
10.1088/0965-0393/7/3/308 / Modell. Simul. Mater. Sci. Eng. (1999)
10.1063/1.2336223 / J. Chem. Phys. (2006)
10.1140/epjb/e2014-50070-0 / Eur. Phys. J. B (2014)
10.1002/qua.24954 / Int. J. Quantum Chem. (2015)
10.1007/BF02478259 / Bull. Math. Biophys. (1943)
10.1021/jp055253z / J. Phys. Chem. A (2006)
10.1002/qua.24890 / Int. J. Quantum Chem. (2015)
10.1063/1.4825111 / J. Chem. Phys. (2013)
10.1103/PhysRevB.28.784 / Phys. Rev. B (1983)
10.1002/qua.24927 / Int. J. Quantum Chem. (2015)
10.1103/PhysRevLett.114.096405 / Phys. Rev. Lett. (2015)
10.1039/b905748j / Phys. Chem. Chem. Phys. (2009)
{'year': '2013', 'key': '2024052420505624800_c57', 'first-page': '121'} (2013)
10.1039/c1cp00051a / Phys. Chem. Chem. Phys. (2011)
10.1016/j.jcp.2014.12.018 / J. Comput. Phys. (2015)
10.1007/BF02551274 / Math. Control, Signals Syst. (1989)
10.1016/0893-6080(91)90009-T / Neural Networks (1991)
10.1039/C6CP00415F / Phys. Chem. Chem. Phys. (2016)
10.1063/1.4940026 / J. Chem. Phys. (2016)
10.1002/qua.21507 / Int. J. Quantum Chem. (2007)
10.1103/PhysRevB.83.153101 / Phys. Rev. B (2011)
10.1103/PhysRevB.92.045131 / Phys. Rev. B (2015)
10.1038/nmat3078 / Nat. Mater. (2011)
10.1103/PhysRevB.86.104301 / Phys. Rev. B (2012)
10.1073/pnas.1602375113 / Proc. Natl. Acad. Sci. U. S. A. (2016)
10.1021/acs.jpclett.6b01448 / J. Phys. Chem. Lett. (2016)
10.1021/nl5005674 / Nano Lett. (2014)
10.1021/acs.jpclett.5b01456 / J. Phys. Chem. Lett. (2015)
10.1039/C6CP05711J / Phys. Chem. Chem. Phys. (2016)

Dates

Type	When
Created	8 years, 9 months ago (Nov. 1, 2016, 8:30 p.m.)
Deposited	1 year, 2 months ago (May 24, 2024, 4:51 p.m.)
Indexed	10 hours, 3 minutes ago (Aug. 22, 2025, 12:55 a.m.)
Issued	8 years, 9 months ago (Nov. 1, 2016)
Published	8 years, 9 months ago (Nov. 1, 2016)
Published Online	8 years, 9 months ago (Nov. 1, 2016)
Published Print	8 years, 9 months ago (Nov. 7, 2016)

Funders 1

Deutsche Forschungsgemeinschaft 10.13039/501100001659
Region: Europe
gov (National government)
Labels3
1. German Research Association
2. German Research Foundation
3. DFG
Awards2
1. Be3264/6-1
2. EXC 1069

BibTeX

@article{Behler_2016, title={Perspective: Machine learning potentials for atomistic simulations}, volume={145}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.4966192}, DOI={10.1063/1.4966192}, number={17}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Behler, Jörg}, year={2016}, month=nov }

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