深度势能方法在材料科学中的应用

doi:10.11900/0412.1961.2024.00141

金属学报

2024, Vol. 60

Issue (10): 1299-1311 DOI: 10.11900/0412.1961.2024.00141

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深度势能方法在材料科学中的应用

文通其(

), 刘怀忆, 龚小国, 叶贝琳, 刘思宇, 李卓远

香港大学机械工程系香港 999077

Deep Potentials for Materials Science

WEN Tongqi(

), LIU Huaiyi, GONG Xiaoguo, YE Beilin, LIU Siyu, LI Zhuoyuan

Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 999077, China

引用本文:

文通其, 刘怀忆, 龚小国, 叶贝琳, 刘思宇, 李卓远. 深度势能方法在材料科学中的应用[J]. 金属学报, 2024, 60(10): 1299-1311.
Tongqi WEN, Huaiyi LIU, Xiaoguo GONG, Beilin YE, Siyu LIU, Zhuoyuan LI. Deep Potentials for Materials Science[J]. Acta Metall Sin, 2024, 60(10): 1299-1311.

全文: PDF(2189 KB) HTML

摘要:

第一性原理计算准确但成本高昂，而建立在传统原子间势函数(力场)基础上的分子动力学模拟速率快但精度低。为了兼顾速率与准确性，机器学习(ML)势函数应运而生并得到广泛应用。深度势能(DP)为ML势的一种，近年来备受关注。本文概述了DP方法在材料科学中的应用。首先介绍了DP的理论基础，随后详细阐述了DP模型的构建和使用，并简要回顾了DP方法在多种材料体系中的应用情况。AIS-Square为DP模型的开发提供了训练数据库及工作流。之后，对比了DP模型与第一性原理计算方法及传统势函数在精度和效率上的表现。最后，对DP方法的发展前景进行了展望。

关键词 ：深度势能, 原子模拟, 机器学习势函数, 神经网络

Abstract：

Although first-principles calculations offer high precision, they are prohibitively expensive. Conversely, molecular dynamics simulations employing classical interatomic potentials, or force fields, offer quicker but less precise outcomes. To balance between computational speed and accuracy, machine learning (ML) potential functions have been developed and have gained widespread application. The deep potential (DP) method, a type of ML potential, has attracted considerable attention recently. This paper provides a comprehensive review of DP methods in materials science. It begins with an introduction to the theoretical foundation of DP, followed by a detailed exposition of the DP model development and usage. Additionally, the application of DP in various material systems is briefly reviewed. AIS-Square contributes training databases and workflows essential for developing DP models. The paper concludes by assessing the performance of DP models relative to both first-principles calculations and classical potentials in terms of accuracy and efficiency. Finally, a brief outlook on future developments trends is provided.

Key words： deep potential atomistic simulation machine learning potential function neural network

收稿日期: 2024-05-06

ZTFLH:

TG148

基金资助:香港大学种子基金项目(2201100392)

通讯作者: 文通其，tongqwen@hku.hk，主要从事结合人工智能方法的材料计算模拟研究

Corresponding author: WEN Tongqi, research assistant professor, Tel: (+852)97049527, E-mail: tongqwen@hku.hk

作者简介: 文通其，男，1993年生，研究助理教授，博士

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https://www.ams.org.cn/CN/10.11900/0412.1961.2024.00141 或 https://www.ams.org.cn/CN/Y2024/V60/I10/1299

图1 DeepPot-SE 和 DPA-1 在不同设置和不同体系上的能量和力的学习曲线[32]

图2 DPA-2下游任务样本效率对比分析[33]

图3 DPA-2蒸馏后的模型在下游体系中的应用测试[33]

图4 Ti DP压缩模型与嵌入原子势(EAM)和修正嵌入原子势(MEAM)函数在CPU和GPU机器上的速率比较[44]

图5 Ga的温度-压力相图[54]

图6 DP和经验势函数H2O相图的计算结果与实验的比较[82]

1	Hafner J. Atomic-scale computational materials science [J]. Acta Mater., 2000, 48: 71
2	Born M, Oppenheimer R. Zur quantentheorie der molekeln [J]. Ann. Phys., 1927, 389: 457
3	Dirac P A M. Quantum mechanics of many-electron systems [J]. Proc. Roy. Soc., 1929, 123A: 714
4	Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects [J]. Phys. Rev., 1965, 140: A1133
5	Verlet L. Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules [J]. Phys. Rev., 1967, 159: 98
6	Zwanzig R W. High-temperature equation of state by a perturbation method. I. Nonpolar gases [J]. J. Chem. Phys., 1954, 22: 1420
7	Tersoff J. Modeling solid-state chemistry: Interatomic potentials for multicomponent systems [J]. Phys. Rev., 1989, 39B: 5566
8	Vink R L C, Barkema G T, van der Weg W F, et al. Fitting the Stillinger-Weber potential to amorphous silicon [J]. J. Non-Cryst. Solids, 2001, 282: 248
9	Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals [J]. Phys. Rev., 1984, 29B: 6443
10	Baskes M I. Modified embedded-atom potentials for cubic materials and impurities [J]. Phys. Rev., 1992, 46B: 2727
11	Prentice J C A, Aarons J, Womack J C, et al. The ONETEP linear-scaling density functional theory program [J]. J. Chem. Phys., 2020, 152: 174111
12	Hacene M, Anciaux-Sedrakian A, Rozanska X, et al. Accelerating VASP electronic structure calculations using graphic processing units [J]. J. Comput. Chem., 2012, 33: 2581 doi: 10.1002/jcc.23096 pmid: 22903247
13	Hutchinson M, Widom M. VASP on a GPU: Application to exact-exchange calculations of the stability of elemental boron [J]. Comput. Phys. Commun., 2012, 183: 1422
14	Jia W L, Cao Z Y, Wang L, et al. The analysis of a plane wave pseudopotential density functional theory code on a GPU machine [J]. Comput. Phys. Commun., 2013, 184: 9
15	Jia W L, Fu J Y, Cao Z Y, et al. Fast plane wave density functional theory molecular dynamics calculations on multi-GPU machines [J]. J. Comput. Phys., 2013, 251: 102
16	Bishop C M. Pattern Recognition and Machine Learning [M]. New York: Springer, 2006: 1122
17	Jordan M I, Mitchell T M. Machine learning: Trends, perspectives, and prospects [J]. Science, 2015, 349: 255 doi: 10.1126/science.aaa8415 pmid: 26185243
18	Mahesh B. Machine learning algorithms-A review [J]. Int. J. Sci. Res., 2020, 9: 381
19	Blank T B, Brown S D, Calhoun A W, et al. Neural network models of potential energy surfaces [J]. J. Chem. Phys., 1995, 103: 4129
20	Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces [J]. Phys. Rev. Lett., 2007, 98: 146401
21	Schütt K T, Sauceda H E, Kindermans P J, et al. SchNet—A deep learning architecture for molecules and materials [J]. J. Chem. Phys., 2018, 148: 241722
22	Schütt K T, Kessel P, Gastegger M, et al. SchNetPack: A deep learning toolbox for atomistic systems [J]. J. Chem. Theory Comput., 2019, 15: 448 doi: 10.1021/acs.jctc.8b00908 pmid: 30481453
23	Ghasemi S A, Hofstetter A, Saha S, et al. Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network [J]. Phys. Rev., 2015, 92B: 045131
24	Hy T S, Trivedi S, Pan H, et al. Predicting molecular properties with covariant compositional networks [J]. J. Chem. Phys., 2018, 148: 241745
25	Unke O T, Meuwly M. PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges [J]. J. Chem. Theory Comput., 2019, 15: 3678 doi: 10.1021/acs.jctc.9b00181 pmid: 31042390
26	Pun G P, Batra R, Ramprasad R, et al. Physically informed artificial neural networks for atomistic modeling of materials [J]. Nat. Commun., 2019, 10: 2339
27	Zuo Y X, Chen C, Li X G, et al. Performance and cost assessment of machine learning interatomic potentials [J]. J. Phys. Chem., 2020, 124A: 731
28	Han J Q, Zhang L F, Car R, et al. Deep potential: A general representation of a many-body potential energy surface [J]. Commun. Comput. Phys., 2018, 23: 629
29	Zhang L F, Han J Q, Wang H, et al. Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics [J]. Phys. Rev. Lett., 2018, 120: 143001
30	Wang H, Zhang L F, Han J Q, et al. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics [J]. Comput. Phys. Commun., 2018, 228: 178
31	Jia W L, Wang H, Chen M H, et al. Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning [A]. Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis [C]. Atlanta: IEEE, 2020: 1
32	Zhang D, Bi H R, Dai F Z, et al. Pretraining of attention-based deep learning potential model for molecular simulation [J]. npj Comput. Mater., 2024, 10: 94
33	Wang H, Zhang D, Liu X Z J, et al. DPA-2: Towards a universal large atomic model for molecular and materials simulation [DB/OL]. arXiv: 2312. 15492, 2024
34	Zhang L F, Han J Q, Wang H, et al. End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems [A]. Advances in Neural Information Processing Systems [C]. Montreal, Canada, Dec.2-8, 2018
35	Perdew J P, Schmidt K. Jacob's ladder of density functional approximations for the exchange-correlation energy [J]. AIP Conf. Proc., 2001, 577: 1
36	DiStasio R A, Santra B, Li Z F, et al. The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water [J]. J. Chem. Phys., 2014, 141: 084502
37	Li Z Y, Wen T Q, Zhang Y Z, et al. An extendable cloud-native alloy property explorer [DB/OL]. arXiv: 2404. 17330, 2024
38	Gasteiger J, Shuaibi M, Sriram A, et al. GemNet-OC: Developing graph neural networks for large and diverse molecular simulation datasets [J]. Trans. Mach. Learn. Res., 2022
39	Lu D H, Wang H, Chen M H, et al. 86 PFLOPS deep potential molecular dynamics simulation of 100 million atoms with ab initio accuracy [J]. Comput. Phys. Commun., 2021, 259: 107624
40	Lu D H, Jiang W R, Chen Y X, et al. DP compress: A model compression scheme for generating efficient deep potential models [J]. J. Chem. Theory Comput., 2022, 18: 5559 doi: 10.1021/acs.jctc.2c00102 pmid: 35926122
41	Wen T Q, Wang R, Zhu L Y, et al. Specialising neural network potentials for accurate properties and application to the mechanical response of titanium [J]. npj Comput. Mater., 2021, 7: 206
42	Mendelev M I, Underwood T L, Ackland G J. Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium [J]. J. Chem. Phys., 2016, 145: 154102
43	Hennig R G, Lenosky T J, Trinkle D R, et al. Classical potential describes martensitic phase transformations between the α, β, and ω titanium phases [J]. Phys. Rev., 2008, 78B: 054121
44	Wen T Q, Zhang L F, Wang H, et al. Deep potentials for materials science [J]. Mater. Futures, 2022, 1: 022601
45	Zhang L F, Lin D Y, Wang H, et al. Active learning of uniformly accurate interatomic potentials for materials simulation [J]. Phys. Rev. Mater., 2019, 3: 023804
46	Wang H, Guo X, Zhang L F, et al. Deep learning inter-atomic potential model for accurate irradiation damage simulations [J]. Appl. Phys. Lett., 2019, 114: 244101
47	Clouet E, Caillard D, Chaari N, et al. Dislocation locking versus easy glide in titanium and zirconium [J]. Nat. Mater., 2015, 14: 931 doi: 10.1038/nmat4340 pmid: 26147845
48	Wang X Y, Wang Y N, Zhang L F, et al. A tungsten deep neural-network potential for simulating mechanical property degradation under fusion service environment [J]. Nucl. Fusion, 2022, 62: 126013
49	Gong X G, Li Z Y, Pattamatta A S L S, et al. An accurate and transferable machine learning interatomic potential for nickel [J]. Commun. Mater., 2024, 5: 157
50	Andolina C M, Bon M, Passerone D, et al. Robust, multi-length-scale, machine learning potential for Ag-Au bimetallic alloys from clusters to bulk materials [J]. J. Phys. Chem., 2021, 125: 17438
51	Wang Y N, Zhang L F, Xu B, et al. A generalizable machine learning potential of Ag-Au nanoalloys and its application to surface reconstruction, segregation and diffusion [J]. Modell. Simul. Mater. Sci. Eng., 2022, 30: 025003
52	Chen B, Zeng Q Y, Wang H, et al. Atomistic mechanism of phase transition in shock compressed gold revealed by deep potential [DB/OL]. arXiv: 2006. 13136, 2020
53	Jiao J Y, Lai G M, Zhao L, et al. Self-healing mechanism of lithium in lithium metal [J]. Adv. Sci., 2022, 9: 2105574
54	Niu H Y, Bonati L, Piaggi P M, et al. Ab initio phase diagram and nucleation of gallium [J]. Nat. Commun., 2020, 11: 2654 doi: 10.1038/s41467-020-16372-9 pmid: 32461573
55	Wang J J, Shen H, Yang R Y, et al. A deep learning interatomic potential developed for atomistic simulation of carbon materials [J]. Carbon, 2022, 186: 1
56	Bonati L, Parrinello M. Silicon liquid structure and crystal nucleation from ab initio deep metadynamics [J]. Phys. Rev. Lett., 2018, 121: 265701
57	Li R, Lee E, Luo T. A unified deep neural network potential capable of predicting thermal conductivity of silicon in different phases [J]. Mater. Today Phys., 2020, 12: 100181
58	Yang M Y, Karmakar T, Parrinello M. Liquid-liquid critical point in phosphorus [J]. Phys. Rev. Lett., 2021, 127: 080603
59	Jain A, Ong S P, Hautier G, et al. Commentary: The materials project: A materials genome approach to accelerating materials innovation [J]. APL Mater., 2013, 1: 011002
60	Wang H D, Zhang Y Z, Zhang L F, et al. Crystal structure prediction of binary alloys via deep potential [J]. Front. Chem., 2020, 8: 589795
61	Andolina C M, Wright J G, Das N, et al. Improved Al-Mg alloy surface segregation predictions with a machine learning atomistic potential [J]. Phys. Rev. Mater., 2021, 5: 083804
62	Jiang W R, Zhang Y Z, Zhang L F, et al. Accurate deep potential model for the Al-Cu-Mg alloy in the full concentration space [J]. Chin. Phys., 2021, 30B: 050706
63	Cao G H, Liang J J, Guo Z L, et al. Liquid metal for high-entropy alloy nanoparticles synthesis [J]. Nature, 2023, 619: 73
64	Bourgeois L, Zhang Y, Zhang Z Z, et al. Transforming solid-state precipitates via excess vacancies [J]. Nat. Commun., 2020, 11: 1248 doi: 10.1038/s41467-020-15087-1 pmid: 32144262
65	Cheng B Q, Zhao X J, Zhang Y, et al. Co-segregation of Mg and Zn atoms at the planar η₁-precipitate/Al matrix interface in an aged Al-Zn-Mg alloy [J]. Scr. Mater., 2020, 185: 51
66	Wen T Q, Wang C Z, Kramer M J, et al. Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds [J]. Phys. Rev., 2019, 100B: 174101
67	Tang L, Yang Z J, Wen T Q, et al. Development of interatomic potential for Al-Tb alloys using a deep neural network learning method [J]. Phys. Chem. Chem. Phys., 2020, 22: 18467 doi: 10.1039/d0cp01689f pmid: 32778859
68	Tang L, Yang Z J, Wen T Q, et al. Short- and medium-range orders in Al₉₀Tb₁₀ glass and their relation to the structures of competing crystalline phases [J]. Acta Mater., 2021, 204: 116513
69	Han I, McKeown J T, Tang L, et al. Dynamic observation of dendritic quasicrystal growth upon laser-induced solid-state transformation [J]. Phys. Rev. Lett., 2020, 125: 195503
70	Tang L, Ho K M, Wang C Z. Molecular dynamics simulation of metallic Al-Ce liquids using a neural network machine learning interatomic potential [J]. J. Chem. Phys., 2021, 155: 194503
71	Balyakin I A, Rempel S V, Ryltsev R E, et al. Deep machine learning interatomic potential for liquid silica [J]. Phys. Rev., 2020, 102E: 052125
72	Wan T Q, Luo C X, Sun Y, et al. Thermoelastic properties of bridgmanite using deep-potential molecular dynamics [J]. Phys. Rev., 2024, 109B: 094101
73	Huang J X, Zhang L F, Wang H, et al. Deep potential generation scheme and simulation protocol for the Li₁₀GeP₂S₁₂-type superionic conductors [J]. J. Chem. Phys., 2021, 154: 094703
74	Ko H Y, Zhang L, Santra B, et al. Isotope effects in liquid water via deep potential molecular dynamics [J]. Mol. Phys., 2019, 117: 3269
75	Zhang C Y, Zhang L F, Xu J H, et al. Isotope effects in x-ray absorption spectra of liquid water [J]. Phys. Rev., 2020, 102B: 115155
76	Xu J H, Zhang C Y, Zhang L F, et al. Isotope effects in molecular structures and electronic properties of liquid water via deep potential molecular dynamics based on the SCAN functional [J]. Phys. Rev., 2020, 102B: 214113
77	Calio P B, Li C H, Voth G A. Resolving the structural debate for the hydrated excess proton in water [J]. J. Am. Chem. Soc., 2021, 143: 18672 doi: 10.1021/jacs.1c08552 pmid: 34723507
78	Sommers G M, Calegari Andrade M F, Zhang L F, et al. Raman spectrum and polarizability of liquid water from deep neural networks [J]. Phys. Chem. Chem. Phys., 2020, 22: 10592 doi: 10.1039/d0cp01893g pmid: 32377657
79	Gartner T E, Zhang L F, Piaggi P M, et al. Signatures of a liquid-liquid transition in an ab initio deep neural network model for water [J]. Proc. Natl. Acad. Sci. USA, 2020, 117: 26040 doi: 10.1073/pnas.2015440117 pmid: 33008883
80	Andreani C, Romanelli G, Parmentier A, et al. Hydrogen dynamics in supercritical water probed by neutron scattering and computer simulations [J]. J. Phys. Chem. Lett., 2020, 11: 9461 doi: 10.1021/acs.jpclett.0c02547 pmid: 33108193
81	Piaggi P M, Panagiotopoulos A Z, Debenedetti P G, et al. Phase equilibrium of water with hexagonal and cubic ice using the SCAN functional [J]. J. Chem. Theory Comput., 2021, 17: 3065 doi: 10.1021/acs.jctc.1c00041 pmid: 33835819
82	Zhang L F, Wang H, Car R, et al. Phase diagram of a deep potential water model [J]. Phys. Rev. Lett., 2021, 126: 236001
83	Aragones J L, Conde M M, Noya E G, et al. 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 [J]. Phys. Chem. Chem. Phys., 2009, 11: 543 doi: 10.1039/b812834k pmid: 19283272
84	Tisi D, Zhang L F, Bertossa R, et al. Heat transport in liquid water from first-principles and deep neural network simulations [J]. Phys. Rev., 2021, 104B: 224202
85	Zhang C Y, Tang F J, Chen M H, et al. Modeling liquid water by climbing up Jacob's ladder in density functional theory facilitated by using deep neural network potentials [J]. J. Phys. Chem., 2021, 125B: 11444
86	Torres A, Pedroza L S, Fernandez-Serra M, et al. Using neural network force fields to ascertain the quality of ab initio simulations of liquid water [J]. J. Phys. Chem., 2021, 125B: 10772
87	Shi Y, Doyle C C, Beck T L. Condensed phase water molecular multipole moments from deep neural network models trained on ab initio simulation data [J]. J. Phys. Chem. Lett., 2021, 12: 10310 doi: 10.1021/acs.jpclett.1c02328 pmid: 34662132
88	Chen M Y, Tan L, Wang H, et al. Imperfectly coordinated water molecules pave the way for homogeneous ice nucleation [DB/OL]. arXiv: 2304. 12665, 2023
89	Xu M Y, Zhu T, Zhang J Z H. Molecular dynamics simulation of zinc ion in water with an ab initio based neural network potential [J]. J. Phys. Chem., 2019, 123A: 6587
90	Niblett S P, Galib M, Limmer D T. Learning intermolecular forces at liquid-vapor interfaces [J]. J. Chem. Phys., 2021, 155: 164101
91	Galib M, Limmer D T. Reactive uptake of N₂O₅ by atmospheric aerosol is dominated by interfacial processes [J]. Science, 2021, 371: 921

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