A Review of Machine Learning Potentials in the Study of Materials Properties
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摘要: 随着人工智能技术与计算硬件的迅速发展，人工智能技术已逐渐成为推动多个科学研究领域变革的革命性工具。在材料科学领域，机器学习方法在材料高通量设计与性能预测方面均发挥着重要作用。近十余年来，基于机器学习构建材料原子间相互作用势的方法已被广泛应用于材料物性研究中，为新型材料的理论设计及微观机制的深入揭示提供了重要支撑。系统梳理了机器学习势的发展历程，介绍其基本流程，概述主流机器学习势的原理及其在材料物性研究中的应用场景，简要评述新兴通用势模型的进展，总结当前面临的挑战及未来发展方向。Abstract: With the rapid advancement of artificial intelligence (AI) technologies and hardware capabilities, AI has gradually become a revolutionary tool driving transformative changes across multiple scientific research domains. In the field of materials science, machine learning methods are significant in high-throughput materials design and property prediction. Over the past decade, machine learning-based approaches for constructing interatomic potentials have been widely applied in the study of material properties, and are providing crucial support for the theoretical design of novel materials and in-depth understanding of their underlying microscopic mechanisms. This article reviews the development of machine learning potentials, and introduces their fundamental workflows. The principles of mainstream methods and their applications in materials property research are outlined. Moreover, recent progress in emerging universal potential models is briefly discussed, then concludes with an analysis of current challenges and future research directions.
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图 7 通过算法、硬件等重新优化下的机器学习势速度提升：(a) Speedup是指用IFORT编译的新SOAP计算与Quippy实现的时序的倒数(tQuippy/tIfort)[28]；(b) 基于GPU的超算平台上液态碳1×109原子的分子动力学模拟中SNAP和ACE的计算效率[36]；(c) AIMD、MLMD与MDPU平台MD的能效对比[37]；(d) 基于Kokkos加速下MTP势计算效率相比原MLIP-3 CPU版本的效率提升[38]
Figure 7. Acceleration of machine learning potentials through optimizations in algorithms and hardware: (a) speedup is defined as the inverse of the time ratio (tQuippy/tIfort) between the new SOAP calculations compiled with IFORT and the implementation by Quippy[28]; (b) the computational efficiency of SNAP and ACE force fields in large-scale molecular dynamics simulations of liquid carbon containing 1×109 atoms on GPU-based supercomputing platforms[36]; (c) a comparison of energy efficiencies among ab initio molecular dynamics (AIMD), machine learning molecular dynamics (MLMD), and MD approaches on the MDPU platform[37]; (d) efficiency gains in MTP potential computations facilitated by Kokkos, as compared to the original CPU version of MLIP-3[38]
图 9 基于机器学习势的材料热输运性质研究：(a) 基于MTP+Boltzmann输运方程给出的二维 ReS2的热导率[80]；(b) 基于GAP和Boltzmann输运方程给出的二维-WS2的热导率[81]；(c)～(d) DP和EMD方法给出的MgSiO3和MgO在高温高压下的热导率图像[82–83]；(e)～(f) 基于NEP+HNEMD方法计算的纳米多孔和非晶碳热导率的密度依赖性[84]
Figure 9. A study of the thermal transport properties of materials based on machine learning potential: (a) thermal conductivity of 2D-ReS2 calculated by the MTP with Boltzmann transport equation[80]; (b) thermal conductivity of 2D-WS2 calculated using the GAP with Boltzmann transport equation[81]; (c)−(d) thermal conductivity map of MgSiO3 at high temperature and pressure calculated by the DP+EMD method[82–83]; (e)−(f) density dependence of the thermal conductivity of nanoporous and amorphous carbon calculated by the NEP+HNEMD method[84]
图 12 MatBench Discovery网站上不同通用势模型基于Materials Project等数据库的综合性能预测评分对比
Figure 12. A comprehensive comparison of the latest performance prediction scores for different general potential models providing on MatBench Discovery’s official website
表 1 常见机器学习势及下载地址
Table 1. Common machine learning potentials and download links
Machine learning potential Download website MTP[13] https://gitlab.com/ashapeev/mlip-2 GAP[18] https://github.com/libAtoms/GAP SNAP[19] https://github.com/FitSNAP/FitSNAP Materials potential library (MatPL) https://github.com/LonxunQuantum/MatPL Machine learning force filed based on VASP (VASP-MLFF)[12] https://www.vasp.at DP[20] https://github.com/deepmodeling/deepmd-kit NEP[22] https://github.com/brucefan1983/GPUMD High-dimensional neural network potential (HDNNP)[7] https://github.com/CompPhysVienna/n2p2 NequIP https://github.com/mir-group/nequip MACE https://github.com/ACEsuit/mace Polarizable atom interaction neural network (PaiNN)[25] https://github.com/atomistic-machine-learning/schnetpack 
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表 2 基于机器学习势的部分材料相变研究汇总[41–42, 44–49, 52–79]
Table 2. A partial overview of studies on machine learning potentials in material phase transitions[41–42, 44–49, 52–79]
MLP Materials Phase transition References MTP U SS/SL Kruglov, et al.[42] (2019) TaVCrW SL Zhu, et al.[52] (2024) Ti-6Al-4V SS/SL Nitol, et al.[53] (2025) Ag-Pd alloy SL Rosenbrock, et al.[54] (2021) Ti, Zr, Hf SS Jung, et al.[55] (2023) U-6%Nb SS Huang, et al.[56] (2025) GAP 2D Ga2O3 SS Zhao, et al.[57] (2021) SiO2 SS Erhard, et al.[58] (2022) Ga2O3 SS/SL Zhao, et al.[59] (2023) Zr SS/SL Zong, et al.[48–49] (2018, 2019) SNAP Carbon SS/SL Willman, et al.[41] (2022) Ni-Mo SS Li, et al.[60] (2018) Au SS/SL Richard, et al.[61] (2023) Co SS Bideault, et al.[62] (2024) VASP-MLFF ZrO2 SS Liu, et al.[63] (2022) Zr SS Liu, et al.[64] (2021) DeepMD H2O SS/SL Zhang, et al.[44] (2021) Hydrogen SS/SL Niu, et al.[65] (2023) H-He LG Dai, et al.[46] (2024) Sn SS/SL Chen, et al.[66] (2023) MgSiO3 SS/SL Deng, et al.[67] (2023) Ag-Pd alloy SS Guo, et al.[68] (2023) MgO SL Wisesa, et al.[69] (2023) SrTiO3 SS He, et al.[70] (2022) Ti SS/SL Wen, et al.[71] (2021) Ga SS/SL Niu, et al.[72] (2020) NEP Coesite SS Feng, et al.[73] (2025) BaZrS3 SS Kayastha, et al.[74] (2025) Oxygen SS/SL Wang, et al.[45] (2025) SiO2 SS Pan, et al.[75] (2024) CsPbBr3, MAPbI3 SS Fransson, et al.[76] (2023) Carbon SS/SL Shi, et al.[47] (2023) MgO-H2O SS Pan, et al.[77] (2023) NequIP Hydrogen LL Istas, et al.[78] (2025) MACE Hydrogen SL LY, et al.[79] (2025)
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表 3 机器学习势在材料热输运性质上的部分研究汇总[81–83, 85–119]
Table 3. Selected studies on machine learning potentials for materials thermal transport properties[81–83, 85–119]
MLP Materials Method References MTP BAs BTE Ouyang, et al.[85] (2022) CoSb3 EMD-GK Korotaev, et al.[86] (2019) SrTiO3 BTE Wang, et al.[87] (2021) 2D materials BTE Mortazavi, et al.[88] (2021) Pb3Bi2S6 BTE Wang, et al.[89] (2025) SnSe EMD-GK Liu, et al.[90] (2021) Cs3Bi2Br9 EMD-GK Li, et al.[91] (2024) 2D ReS2 BTE Yang, et al.[80] (2024) GAP 2D h-BN BTE Zhang, et al.[92] (2021) TiO2 EMD-GK Ren, et al.[93] (2025) h-BN BTE Tang, et al.[94] (2023) 2D-WS2 BTE Zhang, et al.[81] (2023) (vacancies) Si BTE Babaei, et al.[96] (2019) c-BAs BTE Tang, et al.[95] (2023) SNAP MoSSe alloy EMD-GK Gu, et al.[97] (2019) ZrB2 EMD-GK Zhang, et al.[98] (2020) VASP-MLFF CsPbBr3 NEMD Lahnsteiner, et al.[99] (2024) meta-stable Si BTE Cui, et al.[100] (2023) DeepMD MgO EMD-GK Qiu, et al.[83] (2025) Ice EMD-GK Qiu, et al.[101] (2023) Ir EMD-GK Bhatt, et al.[102] (2024) La2Hf2O7 BTE Che, et al.[103] (2024) V EMD-GK Malgope, et al.[104] (2024) MgSiO3-H2O EMD-GK Peng, et al.[105] (2024) SnSe BTE Zhang, et al.[106] (2024) Ice EMD-GK Qiu, et al.[101] (2023) Wadsleyite NEMD Wang, et al.[107] (2022) 2D NiN2 BTE Mirchi, et al.[108] (2024) Bi2Te3 EMD-GK Zhang, et al.[109] (2022) MgSiO3 EMD-GK Yang, et al.[82] (2022) NEP MoS2/WSe2 HNEMD Hu, et al.[110] (2025) ICOF-Li/Na HNEMD Li, et al.[111] (2025) MECs HNEMD Zhou, et al.[112] (2025) BaTiS3 HNEMD Wang, et al.[113] (2025) HECs HNEMD Liu, et al.[114] (2025) 2D PCn HNEMD Cao, et al.[115] (2024) Amorphous Si HNEMD Yang, et al.[116] (2025) HKUST-1 HNEMD Fan, et al.[117] (2024) Mg3(Sb, Bi)2 HNEMD Huang, et al.[118] (2024) Ga2O3/h-BN NEMD So, et al.[119] (2024)
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表 4 机器学习势在材料力学性质上的部分研究汇总[98, 125–126, 129–158]
Table 4. Selected studies on machine learning potentials for mechanical properties of materials[98, 125–126, 129–158]
MLP Materials Properties References MTP β-Ti Elastic Shapeev, et al.[129] (2020) Nb Dislocation Zotov, et al.[130] (2024) U Elastic Wang, et al.[125] (2022) TiZrHfTax Elastic Gubaev, et al.[131] (2021) Poly-carbon Elastic Jalolov, et al.[132] (2024) α-Ag2S Plasticity Yang, et al.[133] (2025) CNTs Mechanical Choyal, et al.[134] (2025) h-BN sheet Strength Choyal, et al.[135] (2025) Ti-Nb-Zr Elastic Mukhamedov, et al.[136] (2025) FeRh Elastic Ourdani, et al.[137] (2024) GAP W/W-Mo Dislocation Koskenniemi, et al.[138] (2023) SNAP Mo, Nb, Ta, W GSFE Wang, et al.[139] (2021) UO2 GSFE Dubois, et al.[140] (2024) Ti3SiC2 MAX Dislocation Hossain, et al.[141] (2023) Mo-Re Elastic Yang, et al.[142] (2024) ZrB2 Elastic Zhang, et al.[98] (2020) Si/MoS2 Friction Wan, et al.[143] (2025) VASP-MLFF CaSiO3 Elastic Zhang, et al.[126] (2025) DeepMD W Mechanical Wang, et al.[144] (2022) MgSiO3 Elastic Wan, et al.[145] (2024) MOF CALF-20 Mechanical Fan, et al.[146] (2024) Cu Dislocation Deng, et al.[147] (2023) CdTe Dislocation Li, et al.[148] (2023) ZrO2 Plasticity Zhang, et al.[149] (2024) MgAlSi Elastic Zhu, et al.[150] (2024) V Mechanical Wang, et al.[151] (2022) H2O Plastic Matusalem, et al.[152] (2022) Ti Dislocation Wen, et al.[153] (2023) Fe Elastic Li, et al.[154] (2022) NEP BeGeN2 Elastic Li, et al.[155] (2025) Ti-Al-Nb GSFE Zhao, et al.[156] (2024) fullerene Strength Ying, et al.[157] (2023) diamane Strength Zhang, et al.[158] (2024)
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