Volume 1 Issue 2
June  2022
Turn off MathJax
Article Contents
Tongqi Wen, Linfeng Zhang, Han Wang, Weinan E, David J Srolovitz. Deep potentials for materials science[J]. Materials Futures, 2022, 1(2): 022601. doi: 10.1088/2752-5724/ac681d
Citation: Tongqi Wen, Linfeng Zhang, Han Wang, Weinan E, David J Srolovitz. Deep potentials for materials science[J]. Materials Futures, 2022, 1(2): 022601. doi: 10.1088/2752-5724/ac681d
shu
Topical Review •
OPEN ACCESS

Deep potentials for materials science

© 2022 The Author(s). Published by IOP Publishing Ltd on behalf of the Songshan Lake Materials Laboratory
Materials Futures, Volume 1, Number 2
  • Received Date: 2022-02-28
  • Accepted Date: 2022-04-19
  • Rev Recd Date: 2022-04-15
  • Publish Date: 2022-05-11
doi: 10.1088/2752-5724/ac681d
  • 1.

    Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, Hong Kong Special Administrative Region of China

  • 2.

    DP Technology, Beijing, People’s Republic of China

  • 3.

    AI for Science Institute, Beijing, People’s Republic of China

  • 4.

    Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, People’s Republic of China

  • 5.

    HEDPS, CAPT, College of Engineering, Peking University, Beijing, People’s Republic of China

  • 6.

    School of Mathematical Sciences, Peking University, Beijing, People’s Republic of China

  • 7.

    Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, United States of America

  • 8.

    International Digital Economy Academy (IDEA), Shenzhen, People’s Republic of China

  • Authors to whom any correspondence should be addressed.

More Information
    Abstract
  • To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e. machine learning potentials (MLPs). One recently developed type of MLP is the deep potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.
    • FullText(HTML)
  • loading
    • References(211)
  • [1]
    Hafner J 2000 Atomic-scale computational materials science Acta Mater. 48 71 doi: 10.1016/S1359-6454(99)00288-8
    [2]
    Born M, Oppenheimer R 1927 Zur quantentheorie der molekeln Ann. Phys., Lpz. 389 457 doi: 10.1002/andp.19273892002
    [3]
    Dirac P A M 1929 Quantum mechanics of many-electron systems Proc. R. Soc. A 123 714 doi: 10.1098/rspa.1929.0094
    [4]
    Kohn W, Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev. 140 A1133 doi: 10.1103/PhysRev.140.A1133
    [5]
    Verlet L 1967 Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules Phys. Rev. 159 98 doi: 10.1103/PhysRev.159.98
    [6]
    Zwanzig R W 1954 High-temperature equation of state by a perturbation method. I. Nonpolar gases J. Chem. Phys. 22 1420 doi: 10.1063/1.1740409
    [7]
    Tersoff J 1989 Modeling solid-state chemistry: interatomic potentials for multicomponent systems Phys. Rev. B 39 5566 doi: 10.1103/PhysRevB.39.5566
    [8]
    Vink R, Barkema G, van der Weg W, Mousseau N 2001 Fitting the Stillinger-Weber potential to amorphous silicon J. Non-Cryst. Solids 282 248 doi: 10.1016/S0022-3093(01)00342-8
    [9]
    Daw M S, Baskes M I 1984 Embedded-atom method: derivation and application to impurities, surfaces and other defects in metals Phys. Rev. B 29 6443 doi: 10.1103/PhysRevB.29.6443
    [10]
    Baskes M I 1992 Modified embedded-atom potentials for cubic materials and impurities Phys. Rev. B 46 2727 doi: 10.1103/PhysRevB.46.2727
    [11]
    Prentice J C A, et al 2020 The ONETEP linear-scaling density functional theory program J. Chem. Phys. 152 174111 doi: 10.1063/5.0004445
    [12]
    Hacene M, Anciaux-Sedrakian A, Rozanska X, Klahr D, Guignon T, Fleurat-Lessard P 2012 Accelerating VASP electronic structure calculations using graphic processing units J. Comput. Chem. 33 2581 doi: 10.1002/jcc.23096
    [13]
    Hutchinson M, Widom M 2012 VASP on a GPU: application to exact-exchange calculations of the stability of elemental boron Comput. Phys. Commun. 183 1422 doi: 10.1016/j.cpc.2012.02.017
    [14]
    Jia W, Cao Z, Wang L, Fu J, Chi X, Gao W, Wang L-W 2013 The analysis of a plane wave pseudopotential density functional theory code on a GPU machine Comput. Phys. Commun. 184 9 doi: 10.1016/j.cpc.2012.08.002
    [15]
    Jia W, Fu J, Cao Z, Wang L, Chi X, Gao W, Wang L-W 2013 Fast plane wave density functional theory molecular dynamics calculations on multi-GPU machines J. Comput. Phys. 251 102 doi: 10.1016/j.jcp.2013.05.005
    [16]
    Bishop C M 2006 Pattern Recognition and Machine LearningNew YorkSpringer
    [17]
    Jordan M I, Mitchell T M 2015 Machine learning: trends, perspectives and prospects Science 349 255 doi: 10.1126/science.aaa8415
    [18]
    Mahesh B 2020 Machine learning algorithms-a review Int. J. Sci. Res. 9 381 doi: 10.21275/ART20203995
    [19]
    Blank T B, Brown S D, Calhoun A W, Doren D J 1995 Neural network models of potential energy surfaces J. Chem. Phys. 103 4129 doi: 10.1063/1.469597
    [20]
    Behler J, Parrinello M 2007 Generalized neural-network representation of high-dimensional potential-energy surfaces Phys. Rev. Lett. 98 146401 doi: 10.1103/PhysRevLett.98.146401
    [21]
    Khaliullin R Z, Eshet H, Khne T D, Behler J, Parrinello M 2011 Nucleation mechanism for the direct graphite-to-diamond phase transition Nat. Mater. 10 693 doi: 10.1038/nmat3078
    [22]
    Artrith N, Urban A 2016 An implementation of artificial neural-network potentials for atomistic materials simulations: performance for TiO2 Comput. Mater. Sci. 114 135 doi: 10.1016/j.commatsci.2015.11.047
    [23]
    Behler J 2021 Four generations of high-dimensional neural network potentials Chem. Rev. 121 10037 doi: 10.1021/acs.chemrev.0c00868
    [24]
    Behler J 2016 Perspective: machine learning potentials for atomistic simulations J. Chem. Phys. 145 170901 doi: 10.1063/1.4966192
    [25]
    Behler J 2017 First principles neural network potentials for reactive simulations of large molecular and condensed systems Angew. Chem., Int. Ed. 56 12828 doi: 10.1002/anie.201703114
    [26]
    Schtt K T, Sauceda H E, Kindermans P-J, Tkatchenko A, Mller K-R 2018 SchNeta deep learning architecture for molecules and materials J. Chem. Phys. 148 241722 doi: 10.1063/1.5019779
    [27]
    Schtt K T, Kessel P, Gastegger M, Nicoli K A, Tkatchenko A, Mller K-R 2019 SchNetPack: a deep learning toolbox for atomistic systems J. Chem. Theory Comput. 15 448 doi: 10.1021/acs.jctc.8b00908
    [28]
    Ghasemi S A, Hofstetter A, Saha S, Goedecker S 2015 Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network Phys. Rev. B 92 045131 doi: 10.1103/PhysRevB.92.045131
    [29]
    Hy T S, Trivedi S, Pan H, Anderson B M, Kondor R 2018 Predicting molecular properties with covariant compositional networks J. Chem. Phys. 148 241745 doi: 10.1063/1.5024797
    [30]
    Unke O T, Meuwly M 2019 Physnet: a neural network for predicting energies, forces, dipole moments and partial charges J. Chem. Theory Comput. 15 3678 doi: 10.1021/acs.jctc.9b00181
    [31]
    Purja Pun G P, Batra R, Ramprasad R, Mishin Y 2019 Physically informed artificial neural networks for atomistic modeling of materials Nat. Commun. 10 2339 doi: 10.1038/s41467-019-10343-5
    [32]
    Bartk A P, Payne M C, Kondor R, Csnyi G 2010 Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons Phys. Rev. Lett. 104 136403 doi: 10.1103/PhysRevLett.104.136403
    [33]
    Dragoni D, Daff T D, Csnyi G, Marzari N 2018 Achieving DFT accuracy with a machine-learning interatomic potential: thermomechanics and defects in bcc ferromagnetic iron Phys. Rev. Mater. 2 013808 doi: 10.1103/PhysRevMaterials.2.013808
    [34]
    Bartk A P, Kermode J, Bernstein N, Csnyi G 2018 Machine learning a general-purpose interatomic potential for silicon Phys. Rev. X 8 041048 doi: 10.1103/PhysRevX.8.041048
    [35]
    Deringer V L, Bartk A P, Bernstein N, Wilkins D M, Ceriotti M, Csnyi G 2021 Gaussian process regression for materials and molecules Chem. Rev. 121 10073 doi: 10.1021/acs.chemrev.1c00022
    [36]
    Shapeev A V 2016 Moment tensor potentials: a class of systematically improvable interatomic potentials Multiscale Model. Simul. 14 1153 doi: 10.1137/15M1054183
    [37]
    Podryabinkin E V, Shapeev A V 2017 Active learning of linearly parametrized interatomic potentials Comput. Mater. Sci. 140 171 doi: 10.1016/j.commatsci.2017.08.031
    [38]
    Podryabinkin E V, Tikhonov E V, Shapeev A V, Oganov A R 2019 Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning Phys. Rev. B 99 064114 doi: 10.1103/PhysRevB.99.064114
    [39]
    Chen C, Deng Z, Tran R, Tang H, Chu I-H, Ong S P 2017 Accurate force field for molybdenum by machine learning large materials data Phys. Rev. Mater. 1 043603 doi: 10.1103/PhysRevMaterials.1.043603
    [40]
    Li X-G, Hu C, Chen C, Deng Z, Luo J, Ong S P 2018 Quantum-accurate spectral neighbor analysis potential models for Ni-Mo binary alloys and fcc metals Phys. Rev. B 98 094104 doi: 10.1103/PhysRevB.98.094104
    [41]
    Deng Z, Chen C, Li X-G, Ong S P 2019 An electrostatic spectral neighbor analysis potential for lithium nitride npj Comput. Mater. 5 75 doi: 10.1038/s41524-019-0212-1
    [42]
    Sauceda H E, Chmiela S, Poltavsky I, Mller K-R, Tkatchenko A 2019 Molecular force fields with gradient-domain machine learning: construction and application to dynamics of small molecules with coupled cluster forces J. Chem. Phys. 150 114102 doi: 10.1063/1.5078687
    [43]
    Chmiela S, Sauceda H E, Poltavsky I, Mller K-R, Tkatchenko A 2019 sGDML: constructing accurate and data efficient molecular force fields using machine learning Comput. Phys. Commun. 240 38 doi: 10.1016/j.cpc.2019.02.007
    [44]
    Unke O T, Chmiela S, Sauceda H E, Gastegger M, Poltavsky I, Schtt K T, Tkatchenko A, Mller K-R 2021 Machine learning force fields Chem. Rev. 121 10142 doi: 10.1021/acs.chemrev.0c01111
    [45]
    Zuo Y, et al 2020 Performance and cost assessment of machine learning interatomic potentials J. Phys. Chem. A 124 731 doi: 10.1021/acs.jpca.9b08723
    [46]
    Han J, Zhang L, Car R, E W 2017 Deep potential: a general representation of a many-body potential energy surface arXiv:1707.01478 [physics.comp-ph])
    [47]
    Han J, Zhang L, Car R, E W 2018 Deep potential: a general representation of a many-body potential energy surface Commun. Comput. Phys. 23 629 doi: 10.4208/cicp.OA-2017-0213
    [48]
    Zhang L, Han J, Wang H, Car R, E W 2018 Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics Phys. Rev. Lett. 120 143001 doi: 10.1103/PhysRevLett.120.143001
    [49]
    Wang H, Zhang L, Han J, E W 2018 Deepmd-kit: a deep learning package for many-body potential energy representation and molecular dynamics Comput. Phys. Commun. 228 178 doi: 10.1016/j.cpc.2018.03.016
    [50]
    Jia W, Wang H, Chen M, Lu D, Lin L, Car R, E W, Zhang L 2020 Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning SC20: Int. Conf. for High Performance Computing, Networking, Storage and Analysis pp 1-14
    [51]
    Artrith N, Morawietz T, Behler J 2011 High-dimensional neural-network potentials for multicomponent systems: applications to zinc oxide Phys. Rev. B 83 153101 doi: 10.1103/PhysRevB.83.153101
    [52]
    Bereau T, Andrienko D, von Lilienfeld O A 2015 Transferable atomic multipole machine learning models for small organic molecules J. Chem. Theory Comput. 11 3225 doi: 10.1021/acs.jctc.5b00301
    [53]
    Bereau T, DiStasio R A, Tkatchenko A, von Lilienfeld O A 2018 Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning J. Chem. Phys. 148 241706 doi: 10.1063/1.5009502
    [54]
    Nebgen B, Lubbers N, Smith J S, Sifain A, Lokhov A, Isayev O, Roitberg A, Barros K, Tretiak S 2018 Transferable molecular charge assignment using deep neural networks arXiv:1803.04395 [physics.chem-ph])
    [55]
    Sifain A E, Lubbers N, Nebgen B T, Smith J S, Lokhov A Y, Isayev O, Roitberg A E, Barros K, Tretiak S 2018 Discovering a transferable charge assignment model using machine learning J. Phys. Chem. Lett. 9 4495 doi: 10.1021/acs.jpclett.8b01939
    [56]
    Ko T W, Finkler J A, Goedecker S, Behler J 2021 A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer Nat. Commun. 12 398 doi: 10.1038/s41467-020-20427-2
    [57]
    Ko T W, Finkler J A, Goedecker S, Behler J 2021 General-purpose machine learning potentials capturing nonlocal charge transfer Acc. Chem. Res. 54 808 doi: 10.1021/acs.accounts.0c00689
    [58]
    Grisafi A, Ceriotti M 2019 Incorporating long-range physics in atomic-scale machine learning J. Chem. Phys. 151 204105 doi: 10.1063/1.5128375
    [59]
    Grisafi A, Nigam J, Ceriotti M 2021 Multi-scale approach for the prediction of atomic scale properties Chem. Sci. 12 2078 doi: 10.1039/D0SC04934D
    [60]
    Frenkel D, Smit B 2002 Understanding Molecular Simulation From Algorithms to ApplicationsNew YorkAcademic
    [61]
    He K, Zhang X, Ren S, Sun J 2016 Deep residual learning for image recognition Proc. Conf. on Computer Vision and Pattern Recognition (CVPR)
    [62]
    Barron A 1993 Universal approximation bounds for superpositions of a sigmoidal function IEEE Trans. Inf. Theory 39 930 doi: 10.1109/18.256500
    [63]
    Barron A R 1994 Approximation and estimation bounds for artificial neural networks Mach. Learn. 14 115 doi: 10.1007/BF00993164
    [64]
    Liang S, Srikant R 2017 Why deep neural networks for function approximation? arXiv:1610.04161 [cs.LG])
    [65]
    Telgarsky M 2016 benefits of depth in neural networks 29th Conf. on Learning Theory (Proc. Machine Learning Research) (PMLR)vol 49ed(V Feldman, A Rakhlin and O Shamir)(New York: Columbia University) 1517-39
    [66]
    Yarotsky D 2017 Error bounds for approximations with deep relu networks Neural Netw. 94 103 doi: 10.1016/j.neunet.2017.07.002
    [67]
    Lu J, Shen Z, Yang H, Zhang S 2021 Deep network approximation for smooth functions SIAM J. Math. Anal. 53 5465 doi: 10.1137/20M134695X
    [68]
    E W, Ma C, Wu L 2019 A priori estimates of the population risk for two-layer neural networks Commun. Math. Sci. 17 1407-25 doi: 10.4310/CMS.2019.v17.n5.a11
    [69]
    E W, Ma C, Wu L 2022 The barron space and the flow-induced function spaces for neural network models Constructive Approx. 55 369-406 doi: 10.1007/s00365-021-09549-y
    [70]
    Zhang L, Han J, Wang H, Saidi W, Car R, E W 2018 End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems Advances in Neural Information Processing Systemsvol 31Bengio S, Wallach H, Larochelle H, Grauman K, Cesa-Bianchi N, Garnett R 2018 (Curran Associates, Inc.) pp 4436-46
    [71]
    Kresse G, Furthmller J 1996 Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Comput. Mater. Sci. 6 15 doi: 10.1016/0927-0256(96)00008-0
    [72]
    Kresse G, Furthmller J 1996 Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B 54 11169 doi: 10.1103/PhysRevB.54.11169
    [73]
    Giannozzi P, et al 2009 QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials J. Phys.: Condens. Matter. 21 395502 doi: 10.1088/0953-8984/21/39/395502
    [74]
    Chen M, Guo G-C, He L 2010 Systematically improvable optimized atomic basis sets for ab initio calculations J. Phys.: Condens. Matter. 22 445501 doi: 10.1088/0953-8984/22/44/445501
    [75]
    Perdew J P, Schmidt K 2001 Jacob’s ladder of density functional approximations for the exchange-correlation energy Conf. Proc.vol 577 p 1
    [76]
    Mller C, Plesset M S 1934 Note on an approximation treatment for many-electron systems Phys. Rev. 46 618 doi: 10.1103/PhysRev.46.618
    [77]
    ek J 1996 On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in ursell-type expansion using quantum-field theoretical methods J. Chem. Phys. 45 4256 doi: 10.1063/1.1727484
    [78]
    Fano U 1961 Effects of configuration interaction on intensities and phase shifts Phys. Rev. 124 1866 doi: 10.1103/PhysRev.124.1866
    [79]
    Deaven D M, Ho K M 1995 Molecular geometry optimization with a genetic algorithm Phys. Rev. Lett. 75 288 doi: 10.1103/PhysRevLett.75.288
    [80]
    Glass C W, Oganov A R, Hansen N 2006 USPEX-evolutionary crystal structure prediction Comput. Phys. Commun. 175 713 doi: 10.1016/j.cpc.2006.07.020
    [81]
    Laio A, Parrinello M 2002 Escaping free-energy minima Proc. Natl Acad. Sci. 99 12562 doi: 10.1073/pnas.202427399
    [82]
    Cohn D, Atlas L, Ladner R 1994 Improving generalization with active learning Mach. Learn. 15 201 doi: 10.1007/BF00993277
    [83]
    Zhang L, Lin D-Y, Wang H, Car R, E W 2019 Active learning of uniformly accurate interatomic potentials for materials simulation Phys. Rev. Mater. 3 023804 doi: 10.1103/PhysRevMaterials.3.023804
    [84]
    Zhang Y, Wang H, Chen W, Zeng J, Zhang L, Wang H, E W 2020 DP-GEN: a concurrent learning platform for the generation of reliable deep learning based potential energy models Comput. Phys. Commun. 253 107206 doi: 10.1016/j.cpc.2020.107206
    [85]
    Plimpton S 1995 Fast parallel algorithms for short-range molecular dynamics J. Comput. Phys. 117 1 doi: 10.1006/jcph.1995.1039
    [86]
    Larsen A H, et al 2017 The atomic simulation environmenta python library for working with atoms J. Phys.: Condens. Matter. 29 273002 doi: 10.1088/1361-648x/aa680e
    [87]
    Ceriotti M, More J, Manolopoulos D E 2014 i-PI: a python interface for ab initio path integral molecular dynamics simulations Comput. Phys. Commun. 185 1019 doi: 10.1016/j.cpc.2013.10.027
    [88]
    Van Der Spoel D, Lindahl E, Hess B, Groenhof G, Mark A E, Berendsen H J C 2005 Gromacs: fast, flexible and free J. Comput. Chem. 26 1701 doi: 10.1002/jcc.20291
    [89]
    Gaussian 16 Revision C.01 2016 Gaussian Inc. Wallingford CT
    [90]
    Soler J M, Artacho E, Gale J D, Garca A, Junquera J, Ordejn P, Snchez-Portal D 2002 The SIESTA method for ab initio order-N materials simulation J. Phys.: Condens. Matter. 14 2745 doi: 10.1088/0953-8984/14/11/302
    [91]
    Khne T D, et al 2020 Cp2k: an electronic structure and molecular dynamics software packagequickstep: efficient and accurate electronic structure calculations J. Chem. Phys. 152 194103 doi: 10.1063/5.0007045
    [92]
    Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X, Reuter K, Scheffler M 2009 Ab initio molecular simulations with numeric atom-centered orbitals Comput. Phys. Commun. 180 2175 doi: 10.1016/j.cpc.2009.06.022
    [93]
    Case D A, Cheatham III T E, Darden T, Gohlke H, Luo R, Merz Jr. K M, Onufriev A, Simmerling C, Wang B, Woods R J 2005 The amber biomolecular simulation programs J. Comput. Chem. 26 1668 doi: 10.1002/jcc.20290
    [94]
    Abadi M, et al 2015 TensorFlow: large-scale machine learning on heterogeneous systems software available fromwww.tensorflow.org/
    [95]
    Zhang L, Wang H, Car R, E W 2021 Phase diagram of a deep potential water model Phys. Rev. Lett. 126 236001 doi: 10.1103/PhysRevLett.126.236001
    [96]
    Schimka L, Gaudoin R, Klime J, Marsman M, Kresse G 2013 Lattice constants and cohesive energies of alkali, alkaline-earth and transition metals: random phase approximation and density functional theory results Phys. Rev. B 87 214102 doi: 10.1103/PhysRevB.87.214102
    [97]
    Kittel C 2005 Introduction to Solid State Physics8th ednNew YorkWiley
    [98]
    Yang M, Karmakar T, Parrinello M 2021 Liquid-liquid critical point in phosphorus Phys. Rev. Lett. 127 080603 doi: 10.1103/PhysRevLett.127.080603
    [99]
    Yang M, Bonati L, Polino D, Parrinello M 2022 Using metadynamics to build neural network potentials for reactive events: the case of urea decomposition in water Catal. Today 387 143 doi: 10.1016/j.cattod.2021.03.018
    [100]
    Jiang W, Zhang Y, Zhang L, Wang H 2021 Accurate Deep Potential model for the Al-Cu-Mg alloy in the full concentration space Chin. Phys. B 30 050706 doi: 10.1088/1674-1056/abf134
    [101]
    Wen T, Wang R, Zhu L, Zhang L, Wang H, Srolovitz D J, Wu Z 2021 Specialising neural network potentials for accurate properties and application to the mechanical response of titanium npj Comput. Mater. 7 206 doi: 10.1038/s41524-021-00661-y
    [102]
    Wang X, Wang Y, Zhang L, Dai F, Wang H 2021 A tungsten deep potential with high accuracy and generalization ability based on a newly designed three-body embedding formalism arXiv:2111.04281 [cond-mat.mtrl-sci])
    [103]
    Wang Y, Zhang L, Xu B, Wang X, Wang H 2022 A generalizable machine learning potential of Ag-Au nanoalloys and its application to surface reconstruction, segregation and diffusion Modelling Simul. Mater. Sci. Eng. 30 025003 doi: 10.1088/1361-651X/ac4002
    [104]
    Fu B, Sun Y, Zhang L, Wang H, Xu B 2021 Deep learning inter-atomic potential for thermal and phonon behaviour of silicon carbide with quantum accuracy arXiv:2110.10843 [cond-mat.mtrl-sci])
    [105]
    Huang J, Zhang L, Wang H, Zhao J, Cheng J, E W 2021 Deep potential generation scheme and simulation protocol for the Li10GeP2S12-type superionic conductors J. Chem. Phys. 154 094703 doi: 10.1063/5.0041849
    [106]
    Lu D, Wang H, Chen M, Lin L, Car R, E W, Jia W, Zhang L 2021 86 PFLOPS deep potential molecular dynamics simulation of 100 million atoms with ab initio accuracy Comput. Phys. Commun. 259 107624 doi: 10.1016/j.cpc.2020.107624
    [107]
    Lu D, Jiang W, Chen Y, Zhang L, Jia W, Wang H, Chen M 2021 DP train, then DP compress: model compression in deep potential molecular dynamics arXiv:2107.02103 [physics.comp-ph])
    [108]
    Mendelev M, Underwood T, Ackland G 2016 Development of an interatomic potential for the simulation of defects, plasticity and phase transformations in titanium J. Chem. Phys. 145 154102 doi: 10.1063/1.4964654
    [109]
    Hennig R, Lenosky T, Trinkle D, Rudin S, Wilkins J W 2008 Classical potential describes martensitic phase transformations between the titanium phases Phys. Rev. B 78 054121 doi: 10.1103/PhysRevB.78.054121
    [110]
    Vtek V 1968 Intrinsic stacking faults in body-centred cubic crystals Phil. Mag. 18 773 doi: 10.1080/14786436808227500
    [111]
    Ko W-S, Grabowski B, Neugebauer J 2015 Development and application of a Ni-Ti interatomic potential with high predictive accuracy of the martensitic phase transition Phys. Rev. B 92 134107 doi: 10.1103/PhysRevB.92.134107
    [112]
    Dickel D, Barrett C, Carino R, Baskes M, Horstemeyer M 2018 Mechanical instabilities in the modeling of phase transitions of titanium Modelling Simul. Mater. Sci. Eng. 26 065002 doi: 10.1088/1361-651X/aac95d
    [113]
    Clouet E, Caillard D, Chaari N, Onimus F, Rodney D 2015 Dislocation locking versus easy glide in titanium and zirconium Nat. Mater. 14 931 doi: 10.1038/nmat4340
    [114]
    Wang H, Guo X, Zhang L, Wang H, Xue J 2019 Deep learning inter-atomic potential model for accurate irradiation damage simulations Appl. Phys. Lett. 114 244101 doi: 10.1063/1.5098061
    [115]
    Zeng Q, Yu X, Yao Y, Gao T, Chen B, Zhang S, Kang D, Wang H, Dai J 2021 Ab initio validation on the connection between atomistic and hydrodynamic description to unravel the ion dynamics of warm dense matter Phys. Rev. Res. 3 033116 doi: 10.1103/PhysRevResearch.3.033116
    [116]
    Liu Q, Lu D, Chen M 2020 Structure and dynamics of warm dense aluminum: a molecular dynamics study with density functional theory and deep potential J. Phys.: Condens. Matter. 32 144002 doi: 10.1088/1361-648x/ab5890
    [117]
    Liu Q, Li J, Chen M 2021 Thermal transport by electrons and ions in warm dense aluminum: a combined density functional theory and deep potential study Matter Radiat. Extremes 6 026902 doi: 10.1063/5.0030123
    [118]
    Cheng Y, et al 2021 Deep-learning potential method to simulate shear viscosity of liquid aluminum at high temperature and high pressure by molecular dynamics AIP Adv. 11 015043 doi: 10.1063/5.0036298
    [119]
    Andolina C M, Bon M, Passerone D, Saidi W A 2021 Robust, multi-length-scale, machine learning potential for Ag-Au bimetallic alloys from clusters to bulk materials J. Phys. Chem. C 125 17438 doi: 10.1021/acs.jpcc.1c04403
    [120]
    Chen B, Zeng Q, Wang H, Zhang S, Kang D, Lu D, Dai J 2021 Atomistic mechanism of phase transition in shock compressed gold revealed by deep potential arXiv:2006.13136 [cond-mat.mtrl-sci])
    [121]
    Jiao J 2021 Self-healing mechanism of lithium in lithium metal batteries arXiv:2106.10979 [cond-mat.mtrl-sci])
    [122]
    Zhang Y, Gao C, Liu Q, Zhang L, Wang H, Chen M 2020 Warm dense matter simulation via electron temperature dependent deep potential molecular dynamics Phys. Plasmas 27 122704 doi: 10.1063/5.0023265
    [123]
    Niu H, Bonati L, Piaggi P M, Parrinello M 2020 Ab initio phase diagram and nucleation of gallium Nat. Commun. 11 1 doi: 10.1038/s41467-020-16372-9
    [124]
    Shi M, Li J, Tao M, Zhang X, Liu J 2021 Artificial intelligence model for efficient simulation of monatomic phase change material antimony Mater. Sci. Semicond. Process. 136 106146 doi: 10.1016/j.mssp.2021.106146
    [125]
    Wang J, Shen H, Yang R, Xie K, Zhang C, Chen L, Ho K-M, Wang C-Z, Wang S 2022 A deep learning interatomic potential developed for atomistic simulation of carbon materials Carbon 186 1 doi: 10.1016/j.carbon.2021.09.062
    [126]
    Bonati L, Parrinello M 2018 Silicon liquid structure and crystal nucleation from ab Initio deep metadynamics Phys. Rev. Lett. 121 265701 doi: 10.1103/PhysRevLett.121.265701
    [127]
    Li R, Lee E, Luo T 2020 A unified deep neural network potential capable of predicting thermal conductivity of silicon in different phases Mater. Today Phys. 12 100181 doi: 10.1016/j.mtphys.2020.100181
    [128]
    Wang H, Zhang Y, Zhang L, Wang H 2020 Crystal structure prediction of binary alloys via deep potential Front. Chem. 8 895 doi: 10.3389/fchem.2020.589795
    [129]
    Andolina C M, Wright J G, Das N, Saidi W A 2021 Improved Al-Mg alloy surface segregation predictions with a machine learning atomistic potential Phys. Rev. Mater. 5 083804 doi: 10.1103/PhysRevMaterials.5.083804
    [130]
    Bourgeois L, Zhang Y, Zhang Z, Chen Y, Medhekar N V 2020 Transforming solid-state precipitates via excess vacancies Nat. Commun. 11 1 doi: 10.1038/s41467-020-15087-1
    [131]
    Cheng B, Zhao X, Zhang Y, Chen H, Polmear I, Nie J-F 2020 Co-segregation of Mg and Zn atoms at the planar 1-precipitate/Al matrix interface in an aged Al-Zn-Mg alloy Scr. Mater. 185 51 doi: 10.1016/j.scriptamat.2020.04.004
    [132]
    Ryltsev R E, Chtchelkatchev N M 2021 Deep machine learning potentials for multicomponent metallic melts: development, predictability and compositional transferability arXiv:2110.14006 [cond-mat.mtrl-sci])
    [133]
    Wen T, et al 2019 Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds Phys. Rev. B 100 174101 doi: 10.1103/PhysRevB.100.174101
    [134]
    Wang Q, Zhai B, Wang H P, Wei B 2021 Atomic structure of liquid refractory Nb5Si3 intermetallic compound alloy based upon deep neural network potential J. Appl. Phys. 130 185103 doi: 10.1063/5.0067157
    [135]
    Guo Y, et al 2019 Bergman-type medium range order in amorphous Zr77Rh23 alloy studied by ab initio molecular dynamics simulations J. Alloys Compd. 790 675 doi: 10.1016/j.jallcom.2019.03.197
    [136]
    Guo Y, et al 2019 Temperature dependence of structural, dynamical and electronic properties of amorphous Bi2Te3: an ab initio study New J. Phys. 21 093062 doi: 10.1088/1367-2630/ab4535
    [137]
    Tang L, Yang Z J, Wen T Q, Ho K M, Kramer M J, Wang C Z 2020 Development of interatomic potential for Al-Tb alloys using a deep neural network learning method Phys. Chem. Chem. Phys. 22 18467 doi: 10.1039/D0CP01689F
    [138]
    Tang L, Yang Z, Wen T, Ho K M, Kramer M J, Wang C Z 2021 Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases Acta Mater. 204 116513 doi: 10.1016/j.actamat.2020.116513
    [139]
    Han I, McKeown J T, Tang L, Wang C-Z, Parsamehr H, Xi Z, Lu Y-R, Kramer M J, Shahani A J 2020 Dynamic observation of dendritic quasicrystal growth upon laser-induced solid-state transformation Phys. Rev. Lett. 125 195503 doi: 10.1103/PhysRevLett.125.195503
    [140]
    Tang L, Ho K M, Wang C Z 2021 Molecular dynamics simulation of metallic Al-Ce liquids using a neural network machine learning interatomic potential J. Chem. Phys. 155 194503 doi: 10.1063/5.0066061
    [141]
    Daniels C L, Liu D-J, Adamson M A S, Knobeloch M, Vela J 2021 Azo(xy) vs aniline selectivity in catalytic nitroarene reduction by intermetallics: experiments and simulations J. Phys. Chem. C 125 24440 doi: 10.1021/acs.jpcc.1c08569
    [142]
    Zhang C, Sun Y, Wang H-D, Zhang F, Wen T-Q, Ho K-M, Wang C-Z 2021 Crystallization of the P3Sn4 phase upon cooling P2Sn5 liquid by molecular dynamics simulation using a machine learning interatomic potential J. Phys. Chem. C 125 3127 doi: 10.1021/acs.jpcc.0c08873
    [143]
    Balyakin I A, Rempel S V, Ryltsev R E, Rempel A A 2020 Deep machine learning interatomic potential for liquid silica Phys. Rev. E 102 052125 doi: 10.1103/PhysRevE.102.052125
    [144]
    Deng J, Stixrude L 2021 Thermal conductivity of silicate liquid determined by machine learning potentials Geophys. Res. Lett. 48 e2021GL093806 doi: 10.1029/2021GL093806
    [145]
    Luo H, Karki B B, Ghosh D B, Bao H 2021 Anomalous behavior of viscosity and electrical conductivity of MgSiO3 melt at mantle conditions Geophys. Res. Lett. 48 e2021GL093573 doi: 10.1029/2021GL093573
    [146]
    Luo H, Karki B B, Ghosh D B, Bao H 2021 Deep neural network potentials for diffusional lithium isotope fractionation in silicate melts Geochim. Cosmochim. Acta 303 38 doi: 10.1016/j.gca.2021.03.031
    [147]
    Chen W, Li L-S 2021 The study of the optical phonon frequency of 3C-SiC by molecular dynamics simulations with deep neural network potential J. Appl. Phys. 129 244104 doi: 10.1063/5.0049464
    [148]
    An Q 2021 Mitigating amorphization in superhard boron carbide by microalloying-induced stacking fault formation Phys. Rev. Mater. 5 103602 doi: 10.1103/PhysRevMaterials.5.103602
    [149]
    Rodriguez A, Lam S, Hu M 2021 Thermodynamic and transport properties of LiF and FLiBe molten salts with deep learning potentials ACS Appl. Mater. Interfaces 13 55367-79 doi: 10.1021/acsami.1c17942
    [150]
    Liang W, Lu G, Yu J 2021 Theoretical prediction on the local structure and transport properties of molten alkali chlorides by deep potentials J. Mater. Sci. Technol. 75 78 doi: 10.1016/j.jmst.2020.09.040
    [151]
    Liang W, Lu G, Yu J 2020 Molecular dynamics simulations of molten magnesium chloride using machine-learning-based deep potential Adv. Theory Simul. 3 2000180 doi: 10.1002/adts.202000180
    [152]
    Pan G, Chen P, Yan H, Lu Y 2020 A DFT accurate machine learning description of molten ZnCl2 and its mixtures: 1. Potential development and properties prediction of molten ZnCl2 Comput. Mater. Sci. 185 109955 doi: 10.1016/j.commatsci.2020.109955
    [153]
    Pan G, Ding J, Du Y, Lee D-J, Lu Y 2021 A DFT accurate machine learning description of molten ZnCl2 and its mixtures: 2. Potential development and properties prediction of ZnCl2-NaCl-KCl ternary salt for CSP Comput. Mater. Sci. 187 110055 doi: 10.1016/j.commatsci.2020.110055
    [154]
    Liang W, Lu G, Yu J 2021 Machine-learning-driven simulations on microstructure and thermophysical properties of MgCl2-KCl eutectic ACS Appl. Mater. Interfaces 13 4034 doi: 10.1021/acsami.0c20665
    [155]
    Bu M, Liang W, Lu G, Yu J 2021 Local structure elucidation and properties prediction on KCl-CaCl2 molten salt: a deep potential molecular dynamics study Sol. Energy Mater. Sol. Cells 232 111346 doi: 10.1016/j.solmat.2021.111346
    [156]
    Zhao J, Liang W, Lu G 2021 Theoretical prediction on the redox potentials of rare-earth ions by deep potentials Ionics 27 2079 doi: 10.1007/s11581-021-03988-0
    [157]
    Zhang J, Fuller J, An Q 2021 Coordination and thermophysical properties of transition metal chlorocomplexes in LiCl-KCl eutectic J. Phys. Chem. B 125 8876 doi: 10.1021/acs.jpcb.1c03748
    [158]
    Xu N, Shi Y, He Y, Shao Q 2020 A deep-learning potential for crystalline and amorphous Li-Si alloys J. Phys. Chem. C 124 16278 doi: 10.1021/acs.jpcc.0c03333
    [159]
    Marcolongo A, Binninger T, Zipoli F, Laino T 2019 Simulating diffusion properties of solid-state electrolytes via a neural network potential: performance and training scheme arXiv:1910.10090 [physics.comp-ph])
    [160]
    Gupta M K, Ding J, Osti N C, Abernathy D L, Arnold W, Wang H, Hood Z, Delaire O 2021 Fast Na diffusion and anharmonic phonon dynamics in superionic Na3PS4 Energy Environ. Sci. 14 6554 doi: 10.1039/D1EE01509E
    [161]
    Li H-X, Zhou X-Y, Wang Y-C, Jiang H 2021 Theoretical study of Na+ transport in the solid-state electrolyte Na3OBr based on deep potential molecular dynamics Inorg. Chem. Front. 8 425 doi: 10.1039/D0QI00921K
    [162]
    Lin M, Liu X, Xiang Y, Wang F, Liu Y, Fu R, Cheng J, Yang Y 2021 Unravelling the fast alkali-ion dynamics in paramagnetic battery materials combined with NMR and deep-potential molecular dynamics simulation Angew. Chem., Int. Ed. 60 12547 doi: 10.1002/anie.202102740
    [163]
    Calegari Andrade M F, Selloni A 2020 Structure of disordered TiO2 phases from ab initio based deep neural network simulations Phys. Rev. Mater. 4 113803 doi: 10.1103/PhysRevMaterials.4.113803
    [164]
    Li R, Liu Z, Rohskopf A, Gordiz K, Henry A, Lee E, Luo T 2020 A deep neural network interatomic potential for studying thermal conductivity of -Ga2O3 Appl. Phys. Lett. 117 152102 doi: 10.1063/5.0025051
    [165]
    Wu J, Zhang Y, Zhang L, Liu S 2021 Deep learning of accurate force field of ferroelectric HfO2 Phys. Rev. B 103 024108 doi: 10.1103/PhysRevB.103.024108
    [166]
    Balyakin I, Sadovnikov S 2022 Deep learning potential for superionic phase of Ag2S Comput. Mater. Sci. 202 110963 doi: 10.1016/j.commatsci.2021.110963
    [167]
    Wang H, Guo X, Xue J 2020 Deep-learning interatomic potential for irradiation damage simulations in MoS2 with ab initial accuracy arXiv:2010.09547 [cond-mat.mtrl-sci])
    [168]
    Guo D, Li C, Li K, Shao B, Chen D, Ma Y, Sun J, Cao X, Zeng W, Chang X 2021 The thermoelectric performance of new structure SnSe studied by quotient graph and deep learning potential Mater. Today Energy 20 100665 doi: 10.1016/j.mtener.2021.100665
    [169]
    Dai F-Z, Wen B, Xiang H, Zhou Y 2020 Grain boundary strengthening in ZrB2 by segregation of W: atomistic simulations with deep learning potential J. Eur. Ceram. Soc. 40 5029 doi: 10.1016/j.jeurceramsoc.2020.06.007
    [170]
    Dai F-Z, Wen B, Sun Y, Xiang H, Zhou Y 2020 Theoretical prediction on thermal and mechanical properties of high entropy (Zr0.2Hf0.2Ti0.2Nb0.2Ta0.2)C by deep learning potential J. Mater. Sci. Technol. 43 168 doi: 10.1016/j.jmst.2020.01.005
    [171]
    Dai F-Z, Sun Y, Wen B, Xiang H, Zhou Y 2021 Temperature dependent thermal and elastic properties of high entropy (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2: molecular dynamics simulation by deep learning potential J. Mater. Sci. Technol. 72 8 doi: 10.1016/j.jmst.2020.07.014
    [172]
    Ko H-Y, Zhang L, Santra B, Wang H, E W, DiStasio Jr R A, Car R 2019 Isotope effects in liquid water via deep potential molecular dynamics Mol. Phys. 117 3269 doi: 10.1080/00268976.2019.1652366
    [173]
    Sommers G M, Calegari Andrade M F, Zhang L, Wang H, Car R 2020 Raman spectrum and polarizability of liquid water from deep neural networks Phys. Chem. Chem. Phys. 22 10592 doi: 10.1039/D0CP01893G
    [174]
    Zhang C, Zhang L, Xu J, Tang F, Santra B, Wu X 2020 Isotope effects in x-ray absorption spectra of liquid water Phys. Rev. B 102 115155 doi: 10.1103/PhysRevB.102.115155
    [175]
    Gartner T E, Zhang L, Piaggi P M, Car R, Panagiotopoulos A Z, Debenedetti P G 2020 Signatures of a liquid-liquid transition in an ab initio deep neural network model for water Proc. Natl Acad. Sci. 117 26040 doi: 10.1073/pnas.2015440117
    [176]
    Andreani C, Romanelli G, Parmentier A, Senesi R, Kolesnikov A I, Ko H-Y, Calegari Andrade M F, Car R 2020 Hydrogen dynamics in supercritical water probed by neutron scattering and computer simulations J. Phys. Chem. Lett. 11 9461 doi: 10.1021/acs.jpclett.0c02547
    [177]
    Xu J, Zhang C, Zhang L, Chen M, Santra B, Wu X 2020 Isotope effects in molecular structures and electronic properties of liquid water via deep potential molecular dynamics based on the SCAN functional Phys. Rev. B 102 214113 doi: 10.1103/PhysRevB.102.214113
    [178]
    Piaggi P M, Panagiotopoulos A Z, Debenedetti P G, Car R 2021 Phase equilibrium of water with hexagonal and cubic ice using the SCAN functional J. Chem. Theory Comput. 17 3065 doi: 10.1021/acs.jctc.1c00041
    [179]
    Tisi D, Zhang L, Bertossa R, Wang H, Car R, Baroni S 2021 Heat transport in liquid water from first-principles and deep-neural-network simulations arXiv:2108.10850 [cond-mat.mtrl-sci])
    [180]
    Zhang C, Tang F, Chen M, Xu J, Zhang L, Qiu D Y, Perdew J P, Klein M L, Wu X 2021 Modeling liquid water by climbing up Jacob’s ladder in density functional theory facilitated by using deep neural network potentials J. Phys. Chem. B 125 11444 doi: 10.1021/acs.jpcb.1c03884
    [181]
    Torres A, Pedroza L S, Fernandez-Serra M, Rocha A R 2021 Using neural network force fields to ascertain the quality of ab initio simulations of liquid water J. Phys. Chem. B 125 10772 doi: 10.1021/acs.jpcb.1c04372
    [182]
    Shi Y, Doyle C C, Beck T L 2021 Condensed phase water molecular multipole moments from deep neural network models trained on ab initio simulation data J. Phys. Chem. Lett. 12 10310 doi: 10.1021/acs.jpclett.1c02328
    [183]
    Calio P B, Li C, Voth G A 2021 Resolving the structural debate for the hydrated excess proton in water J. Am. Chem. Soc. 143 18672 doi: 10.1021/jacs.1c08552
    [184]
    Xu M, Zhu T, Zhang J Z H 2019 Molecular dynamics simulation of zinc ion in water with an ab initio based neural network potential J. Phys. Chem. A 123 6587 doi: 10.1021/acs.jpca.9b04087
    [185]
    Niblett S P, Galib M, Limmer D T 2021 Learning intermolecular forces at liquid-vapor interfaces J. Chem. Phys. 155 164101 doi: 10.1063/5.0067565
    [186]
    Galib M, Limmer D T 2021 Reactive uptake of N2O5 by atmospheric aerosol is dominated by interfacial processes Science 371 921 doi: 10.1126/science.abd7716
    [187]
    Andrade M F C, Ko H-Y, Zhang L, Car R, Selloni A 2020 Free energy of proton transfer at the water-TiO2 interface from ab initio deep potential molecular dynamics Chem. Sci. 11 2335 doi: 10.1039/C9SC05116C
    [188]
    Piaggi P M, Car R 2021 Enhancing the formation of ionic defects to study the ice Ih/XI transition with molecular dynamics simulations Mol. Phys. 119 e1916634 doi: 10.1080/00268976.2021.1916634
    [189]
    Ye Q-J, Zhuang L, Li X-Z 2021 Dynamic nature of high-pressure ice VII Phys. Rev. Lett. 126 185501 doi: 10.1103/PhysRevLett.126.185501
    [190]
    Jiang S, Liu Y-R, Huang T, Feng Y-J, Wang C-Y, Wang Z-Q, Huang W 2021 Towards fully ab initio simulation of atmospheric aerosol nucleation arXiv:2107.04802 [physics.atm-clus])
    [191]
    Zeng J, Zhang L, Wang H, Zhu T 2021 Exploring the chemical space of linear alkane pyrolysis via deep potential generator Energy Fuels 35 762 doi: 10.1021/acs.energyfuels.0c03211
    [192]
    Chen W-K, Liu X-Y, Fang W-H, Dral P O, Cui G 2018 Deep learning for nonadiabatic excited-state dynamics J. Phys. Chem. Lett. 9 6702 doi: 10.1021/acs.jpclett.8b03026
    [193]
    Zhang L, Wang H, E W 2018 Reinforced dynamics for enhanced sampling in large atomic and molecular systems J. Chem. Phys. 148 124113 doi: 10.1063/1.5019675
    [194]
    Wang S, Ma Z, Pan W 2020 Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved Soft Matter 16 8330 doi: 10.1039/D0SM01019G
    [195]
    Pan X, Yang J, Van R, Epifanovsky E, Ho J, Huang J, Pu J, Mei Y, Nam K, Shao Y 2021 Machine-learning-assisted free energy simulation of solution-phase and enzyme reactions J. Chem. Theory Comput. 17 5745 doi: 10.1021/acs.jctc.1c00565
    [196]
    Tuo P, Ye X B, Pan B C 2020 A machine learning based deep potential for seeking the low-lying candidates of Al clusters J. Chem. Phys. 152 114105 doi: 10.1063/5.0001491
    [197]
    Achar S K, Zhang L, Johnson J K 2021 Efficiently trained deep learning potential for graphane J. Phys. Chem. C 125 14874 doi: 10.1021/acs.jpcc.1c01411
    [198]
    Wu J, Bai L, Huang J, Ma L, Liu J, Liu S 2021 Accurate force field of two-dimensional ferroelectrics from deep learning Phys. Rev. B 104 174107 doi: 10.1103/PhysRevB.104.174107
    [199]
    Chen H, Chen J, Ning P, Chen X, Liang J, Yao X, Chen D, Qin L, Huang Y, Wen Z 2021 2D heterostructure of amorphous CoFeB coating black phosphorus nanosheets with optimal oxygen intermediate absorption for improved electrocatalytic water oxidation ACS Nano 15 12418 doi: 10.1021/acsnano.1c04715
    [200]
    Pascuet M, Fernndez J 2015 Atomic interaction of the MEAM type for the study of intermetallics in the Al-U alloy J. Nucl. Mater. 467 229 doi: 10.1016/j.jnucmat.2015.09.030
    [201]
    Jacobsen K W, Norskov J K, Puska M J 1987 Interatomic interactions in the effective-medium theory Phys. Rev. B 35 7423 doi: 10.1103/PhysRevB.35.7423
    [202]
    Jain A, et al 2013 Commentary: The materials project: a materials genome approach to accelerating materials innovation APL Mater. 1 011002 doi: 10.1063/1.4812323
    [203]
    Wang Y, Lv J, Zhu L, Ma Y 2012 Calypso: a method for crystal structure prediction Comput. Phys. Commun. 183 2063 doi: 10.1016/j.cpc.2012.05.008
    [204]
    Aragones J L, Conde M M, Noya E G, Vega C 2009 The phase diagram of water at high pressures as obtained by computer simulations of the tip4p/2005 model: the appearance of a plastic crystal phase Phys. Chem. Chem. Phys. 11 543 doi: 10.1039/B812834K
    [205]
    Poschmann M, Asta M, Chrzan D C 2018 Convergence of calculated dislocation core structures in hexagonal close packed titanium Modelling Simul. Mater. Sci. Eng. 26 014003 doi: 10.1088/1361-651X/aa9ba9
    [206]
    Queyroux J-A, et al 2020 Melting curve and isostructural solid transition in superionic ice Phys. Rev. Lett. 125 195501 doi: 10.1103/PhysRevLett.125.195501
    [207]
    Mishin Y 2021 Machine-learning interatomic potentials for materials science Acta Mater. 214 116980 doi: 10.1016/j.actamat.2021.116980
    [208]
    Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser L, Polosukhin I 2017 Attention is all you need available at: https://doi.org/10.48550/ARXIV.1706.03762
    [209]
    Devlin J, Chang M-W, Lee K, Toutanova K 2019 Bert: pre-training of deep bidirectional transformers for language understanding Proc. 2019th Conf. North American Chapter of the Association for Computational Linguistics: Human Language Technologies, (Long and Short Papers Vol 1)Minneapolis, MN(Association for Computational Linguistics) pp 4171-86
    [210]
    Brown T, et al 2020 Language models are few-shot learners Adv. Neural Inf. Process. Syst. 33 1877-901
    [211]
    Min B, Ross H, Sulem E, Veyseh A P B, Nguyen T H, Sainz O, Agirre E, Heinz I, Roth D 2021 Recent advances in natural language processing via large pre-trained language models: a survey available at:https://doi.org/10.48550/ARXIV.2111.01243
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    Figures(12)  / Tables(2)

    Citation Export
    PDF
    XML

    Article Metrics

    Article Views(1617) PDF downloads(342)
    Article Statistics
    Related articles from

    Quick Links

    Contact Us

    • Building A1, Songshan Lake International Innovation Entrepreneurship Community, Dongguan, Guangdong
    • E-mail：editorialoffice@materialsfutures.org
    • Tel：+86-769-89136721

    Relevant Links

    WeChat

    Copyright © 2021 Materials Futures Editorial Office

    Supported by: Beijing Renhe Information Technology Co., Ltd.    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return