Deep learning in two-dimensional materials: Characterization, prediction, and design

Abstract

Since the isolation of graphene, two-dimensional (2D) materials have attracted increasing interest because of their excellent chemical and physical properties, as well as promising applications. Nonetheless, particular challenges persist in their further development, particularly in the effective identification of diverse 2D materials, the domains of large-scale and high-precision characterization, also intelligent function prediction and design. These issues are mainly solved by computational techniques, such as density function theory and molecular dynamic simulation, which require powerful computational resources and high time consumption. The booming deep learning methods in recent years offer innovative insights and tools to address these challenges. This review comprehensively outlines the current progress of deep learning within the realm of 2D materials. Firstly, we will briefly introduce the basic concepts of deep learning and commonly used architectures, including convolutional neural and generative adversarial networks, as well as U-net models. Then, the characterization of 2D materials by deep learning methods will be discussed, including defects and materials identification, as well as automatic thickness characterization. Thirdly, the research progress for predicting the unique properties of 2D materials, involving electronic, mechanical, and thermodynamic features, will be evaluated succinctly. Lately, the current works on the inverse design of functional 2D materials will be presented. At last, we will look forward to the application prospects and opportunities of deep learning in other aspects of 2D materials. This review may offer some guidance to boost the understanding and employing novel 2D materials.

Graphical abstract

Keywords

deep learning / two-dimensional materials / materials identification / thickness characterization / prediction / inverse design / convolutional neural networks / generative adversarial networks

References

[1] K. S. Novoselov , A. K. Geim , S. V. Morozov , D. Jiang , Y. Zhang , S. V. Dubonos , I. V. Grigorieva , A. A. Firsov . Electric field effect in atomically thin carbon films. Science, 2004, 306(5696): 666

[2] Q. Ma , G. Ren , K. Xu , J. Z. Ou . Tunable optical properties of 2D materials and their applications. Adv. Opt. Mater., 2021, 9(2): 2001313

[3] X. L. Li , W. P. Han , J. B. Wu , X. F. Qiao , J. Zhang , P. H. Tan . Layer-number dependent optical properties of 2D materials and their application for thickness determination. Adv. Funct. Mater., 2017, 27(19): 1604468

[4] T. Low , A. Chaves , J. D. Caldwell , A. Kumar , N. X. Fang , P. Avouris , T. F. Heinz , F. Guinea , L. Martin-Moreno , F. Koppens . Polaritons in layered two-dimensional materials. Nat. Mater., 2017, 16(2): 182

[5] Y. Qin , M. Sayyad , A. R. P. Montblanch , M. S. G. Feuer , D. Dey , M. Blei , R. Sailus , D. M. Kara , Y. Shen , S. Yang , A. S. Botana , M. Atature , S. Tongay . Reaching the excitonic limit in 2D Janus monolayers by in situ deterministic growth. Adv. Mater., 2022, 34(6): 2106222

[6] T. LaMountain , E. J. Lenferink , Y. J. Chen , T. K. Stanev , N. P. Stern . Environmental engineering of transition metal dichalcogenide optoelectronics. Front. Phys., 2018, 13(4): 138114

[7] Y. Liu , C. Xiao , Z. Li , Y. Xie . Vacancy engineering for tuning electron and phonon structures of two-dimensional materials. Adv. Energy Mater., 2016, 6(23): 1600436

[8] A. Kuc , T. Heine , A. Kis . Electronic properties of transition-metal dichalcogenides. MRS Bull., 2015, 40(7): 577

[9] Q. H. Wang , K. Kalantar-Zadeh , A. Kis , J. N. Coleman , M. S. Strano . Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol., 2012, 7(11): 699

[10] Y.Q. FangF.K. WangR.Q. WangT.ZhaiF.Huang, 2D NbOI₂: A chiral semiconductor with highly in-plane anisotropic electrical and optical properties, Adv. Mater. 33(29), 2101505 (2021)

[11] R. Yang , J. Fan , M. Sun . Transition metal dichalcogenides (TMDCs) heterostructures: Optoelectric properties. Front. Phys., 2022, 17(4): 43202

[12] H. Song , J. Liu , B. Liu , J. Wu , H. M. Cheng , F. Kang . Two-dimensional materials for thermal management applications. Joule, 2018, 2(3): 442

[13] Y. Wang , N. Xu , D. Li , J. Zhu . Thermal properties of two dimensional layered materials. Adv. Funct. Mater., 2017, 27(19): 1604134

[14] L. Thiel , Z. Wang , M. A. Tschudin , D. Rohner , I. Gutiérrez-Lezama , N. Ubrig , M. Gibertini , E. Giannini , A. F. Morpurgo , P. Maletinsky . Probing magnetism in 2D materials at the nanoscale with single-spin microscopy. Science, 2019, 364(6444): 973

[15] Y. Li , B. Yang , S. Xu , B. Huang , W. Duan . Emergent phenomena in magnetic two-dimensional materials and van der Waals heterostructures. ACS Appl. Electron. Mater., 2022, 4(7): 3278

[16] M. Gibertini , M. Koperski , A. F. Morpurgo , K. S. Novoselov . Magnetic 2D materials and heterostructures. Nat. Nanotechnol., 2019, 14(5): 408

[17] X. Li , M. Sun , C. Shan , Q. Chen , X. Wei . Mechanical properties of 2D materials studied by in situ microscopy techniques. Adv. Mater. Interfaces, 2018, 5(5): 1701246

[18] H. Jiang , L. Zheng , Z. Liu , X. Wang . Two-dimensional materials: From mechanical properties to flexible mechanical sensors. InfoMat, 2020, 2(6): 1077

[19] C. Fang , H. Wang , Z. Shen , H. Shen , S. Wang , J. Ma , J. Wang , H. Luo , D. Li . High-performance photodetectors based on lead-free 2D Ruddlesden–Popper perovskite/MoS₂ heterostructures. ACS Appl. Mater. Interfaces, 2019, 11(8): 8419

[20] H. Liu , X. Zhu , X. Sun , C. Zhu , W. Huang , X. Zhang , B. Zheng , Z. Zou , Z. Luo , X. Wang , D. Li , A. Pan . Self-powered broad-band photodetectors based on vertically stacked WSe₂/Bi₂Te₃ p–n heterojunctions. ACS Nano, 2019, 13(11): 13573

[21] M. Long , A. Gao , P. Wang , H. Xia , C. Ott , C. Pan , Y. Fu , E. Liu , X. Chen , W. Lu , T. Nilges , J. Xu , X. Wang , W. Hu , F. Miao . Room temperature high-detectivity mid-infrared photodetectors based on black arsenic phosphorus. Sci. Adv., 2017, 3(6): e1700589

[22] S. Das , D. Pandey , J. Thomas , T. Roy . The role of graphene and other 2D materials in solar photovoltaics. Adv. Mater., 2019, 31(1): 1802722

[23] A. Abnavi , R. Ahmadi , H. Ghanbari , M. Fawzy , A. Hasani , T. De Silva , A. M. Askar , M. R. Mohammadzadeh , F. Kabir , M. Whitwick , M. Beaudoin , S. K. O’Leary , M. M. Adachi . Flexible high-performance photovoltaic devices based on 2D MoS₂ diodes with geometrically asymmetric contact areas. Adv. Funct. Mater., 2023, 33(7): 2210619

[24] J. Sung , D. Shin , H. Cho , S. W. Lee , S. Park , Y. D. Kim , J. S. Moon , J. H. Kim , S. H. Gong . Room-temperature continuous-wave indirect-bandgap transition lasing in an ultra-thin WS₂ disk. Nat. Photonics, 2022, 16(11): 792

[25] C. Li , L. Zhao , Q. Shang , R. Wang , P. Bai , J. Zhang , Y. Gao , Q. Cao , Z. Wei , Q. Zhang . Room-temperature near-infrared excitonic lasing from mechanically exfoliated InSe microflake. ACS Nano, 2022, 16(1): 1477

[26] J.GuB.ChakrabortyM.KhatoniarV.M. Menon, A room-temperature polariton light-emitting diode based on monolayer WS₂, Nat. Nanotechnol. 14(11), 1024 (2019)

[27] L. Zhao , Y. Jiang , C. Li , Y. Liang , Z. Wei , X. Wei , Q. Zhang . Probing anisotropic deformation and near-infrared emission tuning in thin-layered InSe crystal under high pressure. Nano Lett., 2023, 23(8): 3493

[28] J. Wang , Y. J. Zhou , D. Xiang , S. J. Ng , K. Watanabe , T. Taniguchi , G. Eda . Polarized light-emitting diodes based on anisotropic excitons in few-layer ReS₂. Adv. Mater., 2020, 32(32): 2001890

[29] D. Jariwala , V. K. Sangwan , L. J. Lauhon , T. J. Marks , M. C. Hersam . Emerging device applications for semiconducting two-dimensional transition metal dichalcogenides. ACS Nano, 2014, 8(2): 1102

[30] G. Fiori , F. Bonaccorso , G. Iannaccone , T. Palacios , D. Neumaier , A. Seabaugh , S. K. Banerjee , L. Colombo . Electronics based on two-dimensional materials. Nat. Nanotechnol., 2014, 9(10): 768

[31] P. Kaushal , G. Khanna . The role of two-dimensional materials for electronic devices. Mater. Sci. Semicond. Process., 2022, 143: 106546

[32] R. Cheng , S. Jiang , Y. Chen , Y. Liu , N. Weiss , H. C. Cheng , H. Wu , Y. Huang , X. Duan . Few-layer molybdenum disulfide transistors and circuits for high-speed flexible electronics. Nat. Commun., 2014, 5(1): 5143

[33] M. Choi , S. R. Bae , L. Hu , A. T. Hoang , S. Y. Kim , J. H. Ahn . Full-color active-matrix organic light-emitting diode display on human skin based on a large-area MoS₂ backplane. Sci. Adv., 2020, 6(28): eabb5898

[34] B. Mukherjee , R. Hayakawa , K. Watanabe , T. Taniguchi , S. Nakaharai , Y. Wakayama . ReS₂/h-BN/graphene heterostructure based multifunctional devices:Tunneling diodes, FETs, logic gates, and memory. Adv. Electron. Mater., 2021, 7(1): 2000925

[35] M. Cheng , J. B. Yang , X. H. Li , H. Li , R. F. Du , J. P. Shi , J. He . Improving the device performances of two-dimensional semiconducting transition metal dichalcogenides: Three strategies. Front. Phys., 2022, 17(6): 63601

[36] X. Hu , G. Wang , J. Li , J. Huang , Y. Liu , G. Zhong , J. Yuan , H. Zhan , Z. Wen . Significant contribution of single atomic Mn implanted in carbon nanosheets to high-performance sodium–ion hybrid capacitors. Energy Environ. Sci., 2021, 14(8): 4564

[37] Z. Huang , H. Hou , Y. Zhang , C. Wang , X. Qiu , X. Ji . Layer-tunable phosphorene modulated by the cation insertion rate as a sodium-storage anode. Adv. Mater., 2017, 29(34): 1702372

[38] X. Lu , Y. Shi , D. Tang , X. Lu , Z. Wang , N. Sakai , Y. Ebina , T. Taniguchi , R. Ma , T. Sasaki , C. Yan . Accelerated ionic and charge transfer through atomic interfacial electric fields for superior sodium storage. ACS Nano, 2022, 16(3): 4775

[39] X. Li , M. Li , Z. Huang , G. Liang , Z. Chen , Q. Yang , Q. Huang , C. Zhi . Activating the I⁰/I⁺ redox couple in an aqueous I₂–Zn battery to achieve a high voltage plateau. Energy Environ. Sci., 2021, 14(1): 407

[40] Y. Zhang , J. Cao , Z. Yuan , L. Zhao , L. Wang , W. Han . Assembling Co₃O₄ nanoparticles into MXene with enhanced electrochemical performance for advanced asymmetric supercapacitors. J. Colloid Interface Sci., 2021, 599: 109

[41] Y. K. Kim , K. Y. Shin . Functionalized phosphorene/polypyrrole hybrid nanomaterial by covalent bonding and its supercapacitor application. J. Ind. Eng. Chem., 2021, 94: 122

[42] Q. Fu , Y. Meng , Z. Fang , Q. Hu , L. Xu , W. Gao , X. Huang , Q. Xue , Y. P. Sun , F. Lu . Boron nitride nanosheet-anchored Pd–Fe core–shell nanoparticles as highly efficient catalysts for suzuki–miyaura coupling reactions. ACS Appl. Mater. Interfaces, 2017, 9(3): 2469

[43] H. H. Shin , E. Kang , H. Park , T. Han , C. H. Lee , D. K. Lim . Pd-nanodot decorated MoS₂ nanosheets as a highly efficient photocatalyst for the visible-light-induced Suzuki–Miyaura coupling reaction. J. Mater. Chem. A, 2017, 5(47): 24965

[44] C. Yao , N. Guo , S. Xi , C. Q. Xu , W. Liu , X. Zhao , J. Li , H. Fang , J. Su , Z. Chen , H. Yan , Z. Qiu , P. Lyu , C. Chen , H. Xu , X. Peng , X. Li , B. Liu , C. Su , S. J. Pennycook , C. J. Sun , J. Li , C. Zhang , Y. Du , J. Lu . Atomically-precise dopant-controlled single cluster catalysis for electrochemical nitrogen reduction. Nat. Commun., 2020, 11(1): 4389

[45] Z. Luo , H. Zhang , Y. Yang , X. Wang , Y. Li , Z. Jin , Z. Jiang , C. Liu , W. Xing , J. Ge . Reactant friendly hydrogen evolution interface based on di-anionic MoS₂ surface. Nat. Commun., 2020, 11(1): 1116

[46] H. J. Li , K. Xi , W. Wang , S. Liu , G. R. Li , X. P. Gao . Quantitatively regulating defects of 2D tungsten selenide to enhance catalytic ability for polysulfide conversion in a lithium sulfur battery. Energy Storage Mater., 2022, 45: 1229

[47] G.ZhangG.LiJ.WangH.TongJ.WangY.DuS.SunF.Dang, 2D SnSe cathode catalyst featuring an efficient facet-dependent selective Li₂O₂ growth/decomposition for Li-oxygen batteries, Adv. Energy Mater. 12(21), 2103910 (2022)

[48] J. Hou , H. Wang , Z. Ge , T. Zuo , Q. Chen , X. Liu , S. Mou , C. Fan , Y. Xie , L. Wang . Treating acute kidney injury with antioxidative black phosphorus nanosheets. Nano Lett., 2020, 20(2): 1447

[49] W. Chen , J. Ouyang , X. Yi , Y. Xu , C. Niu , W. Zhang , L. Wang , J. Sheng , L. Deng , Y. N. Liu , S. Guo . Black phosphorus nanosheets as a neuroprotective nanomedicine for neurodegenerative disorder therapy. Adv. Mater., 2018, 30(3): 1703458

[50] D. Yim , D. E. Lee , Y. So , C. Choi , W. Son , K. Jang , C. S. Yang , J. H. Kim . Sustainable nanosheet antioxidants for sepsis therapy via scavenging intracellular reactive oxygen and nitrogen species. ACS Nano, 2020, 14(8): 10324

[51] W.FengX.HanH.HuM.ChangL.DingH.XiangY.ChenY.Li, 2D vanadium carbide MXenzyme to alleviate ROS-mediated inflammatory and neurodegenerative diseases, Nat. Commun. 12(1), 2203 (2021)

[52] M. Li , X. Peng , Y. Han , L. Fan , Z. Liu , Y. Guo . Ti₃C₂ MXenes with intrinsic peroxidase-like activity for label-free and colorimetric sensing of proteins. Microchem. J., 2021, 166: 106238

[53] K. Rasool , M. Helal , A. Ali , C. E. Ren , Y. Gogotsi , K. A. Mahmoud . Antibacterial activity of Ti₃C₂T_x MXene. ACS Nano, 2016, 10(3): 3674

[54] A. Arabi Shamsabadi , M. Sharifian Gh , B. Anasori , M. Soroush . Antimicrobial mode-of-action of colloidal Ti₃C₂T_x MXene nanosheets. ACS Sustain. Chem. & Eng., 2018, 6(12): 16586

[55] R. Sha , T. K. Bhattacharyya . MoS₂-based nanosensors in biomedical and environmental monitoring applications. Electrochim. Acta, 2020, 349: 136370

[56] H. K. Choi , J. Park , O. H. Gwon , J. Y. Kim , S. J. Kang , H. R. Byun , B. K. Shin , S. G. Jang , H. S. Kim , Y. J. Yu . Gate-tuned gas molecule sensitivity of a two-dimensional semiconductor. ACS Appl. Mater. Interfaces, 2022, 14(20): 23617

[57] S. P. Figerez , K. K. Tadi , K. R. Sahoo , R. Sharma , R. K. Biroju , A. Gigi , K. A. Anand , G. Kalita , T. N. Narayanan . Molybdenum disulfide–graphene van der Waals heterostructures as stable and sensitive electrochemical sensing platforms. Tungsten, 2020, 2(4): 411

[58] R. Madhuvilakku , S. Alagar , R. Mariappan , S. Piraman . Glassy carbon electrodes modified with reduced graphene oxide-MoS₂-poly (3, 4-ethylene dioxythiophene) nanocomposites for the non-enzymatic detection of nitrite in water and milk. Anal. Chim. Acta, 2020, 1093: 93

[59] L. Wu , Q. Wang , B. Ruan , J. Zhu , Q. You , X. Dai , Y. Xiang . High-performance lossy-mode resonance sensor based on few-layer black phosphorus. J. Phys. Chem. C, 2018, 122(13): 7368

[60] C.H. HuangT.T. HuangC.H. ChiangW.T. HuangY.T. Lin, A chemiresistive biosensor based on a layered graphene oxide/graphene composite for the sensitive and selective detection of circulating miRNA-21, Biosens. Bioelectron. 164, 112320 (2020)

[61] S. Cui , H. Pu , S. A. Wells , Z. Wen , S. Mao , J. Chang , M. C. Hersam , J. Chen . Ultrahigh sensitivity and layer-dependent sensing performance of phosphorene-based gas sensors. Nat. Commun., 2015, 6(1): 8632

[62] Q. Liang , Q. Wang , Q. Zhang , J. Wei , S. X. Lim , R. Zhu , J. Hu , W. Wei , C. Lee , C. H. Sow , W. Zhang , A. T. S. Wee . High-performance, room temperature, ultra-broadband photodetectors based on air-stable PdSe₂. Adv. Mater., 2019, 31(24): 1807609

[63] Y. Wang , L. Li , W. Yao , S. Song , J. T. Sun , J. Pan , X. Ren , C. Li , E. Okunishi , Y. Q. Wang , E. Wang , Y. Shao , Y. Y. Zhang , H. Yang , E. F. Schwier , H. Iwasawa , K. Shimada , M. Taniguchi , Z. Cheng , S. Zhou , S. Du , S. J. Pennycook , S. T. Pantelides , H. J. Gao . Monolayer PtSe₂, a new semiconducting transition-metal-dichalcogenide, epitaxially grown by direct selenization of Pt. Nano Lett., 2015, 15(6): 4013

[64] X. Yu , P. Yu , D. Wu , B. Singh , Q. Zeng , H. Lin , W. Zhou , J. Lin , K. Suenaga , Z. Liu , Q. J. Wang . Atomically thin noble metal dichalcogenide: A broadband mid-infrared semiconductor. Nat. Commun., 2018, 9(1): 1545

[65] A. D. Oyedele , S. Yang , L. Liang , A. A. Puretzky , K. Wang , J. Zhang , P. Yu , P. R. Pudasaini , A. W. Ghosh , Z. Liu , C. M. Rouleau , B. G. Sumpter , M. F. Chisholm , W. Zhou , P. D. Rack , D. B. Geohegan , K. Xiao . PdSe₂: Pentagonal two-dimensional layers with high air stability for electronics. J. Am. Chem. Soc., 2017, 139(40): 14090

[66] Y. Gong , Z. Lin , Y. X. Chen , Q. Khan , C. Wang , B. Zhang , G. Nie , N. Xie , D. Li . Two-dimensional platinum diselenide: Synthesis, emerging applications, and future challenges. Nano-Micro Lett., 2020, 12(1): 174

[67] Y. Wang , Y. Li , Z. Chen . Not your familiar two dimensional transition metal disulfide: structural and electronic properties of the PdS₂ monolayer. J. Mater. Chem. C, 2015, 3(37): 9603

[68] M.Ghorbani-AslA.KucP.MiroT.Heine, A single-material logical junction based on 2D crystal PdS₂, Adv. Mater. 28(5), 853 (2016)

[69] Y. Zhao , J. Qiao , P. Yu , Z. Hu , Z. Lin , S. P. Lau , Z. Liu , W. Ji , Y. Chai . Extraordinarily strong interlayer interaction in 2D layered PtS₂. Adv. Mater., 2016, 28(12): 2399

[70] X. Chia , A. Adriano , P. Lazar , Z. Sofer , J. Luxa , M. Pumera . Layered platinum dichalcogenides (PtS₂, PtSe₂, and PtTe₂) electrocatalysis: Monotonic dependence on the chalcogen size. Adv. Funct. Mater., 2016, 26(24): 4306

[71] Y. Wang , L. Zhou , M. Zhong , Y. Liu , S. Xiao , J. He . Two-dimensional noble transition-metal dichalcogenides for nanophotonics and optoelectronics: Status and prospects. Nano Res., 2022, 15(4): 3675

[72] L. Pi , L. Li , K. Liu , Q. Zhang , H. Li , T. Zhai . Recent progress on 2D noble-transition-metal dichalcogenides. Adv. Funct. Mater., 2019, 29(51): 1904932

[73] H. Zeng , Y. Wen , L. Yin , R. Q. Cheng , H. Wang , C. S. Liu , J. He . Recent developments in CVD growth and applications of 2D transition metal dichalcogenides. Front. Phys., 2023, 18(5): 53603

[74] W. Wu , G. Qiu , Y. Wang , R. Wang , P. Ye . Tellurene: Its physical properties, scalable nanomanufacturing, and device applications. Chem. Soc. Rev., 2018, 47(19): 7203

[75] Y. Wang , G. Qiu , R. Wang , S. Huang , Q. Wang , Y. Liu , Y. Du , W. A. III Goddard , M. J. Kim , X. Xu , P. D. Ye , W. Wu . Field-effect transistors made from solution-grown two-dimensional tellurene. Nat. Electron., 2018, 1(4): 228

[76] Z. Xie , C. Xing , W. Huang , T. Fan , Z. Li , J. Zhao , Y. Xiang , Z. Guo , J. Li , Z. Yang , B. Dong , J. Qu , D. Fan , H. Zhang . Ultrathin 2D nonlayered tellurium nanosheets: Facile liquid-phase exfoliation, characterization, and photoresponse with high performance and enhanced stability. Adv. Funct. Mater., 2018, 28(16): 1705833

[77] W. Gao , Z. Zheng , P. Wen , N. Huo , J. Li . Novel two-dimensional monoelemental and ternary materials: Growth, physics and application. Nanophotonics, 2020, 9(8): 2147

[78] L. Xian , A. Pérez Paz , E. Bianco , P. M. Ajayan , A. Rubio . Square selenene and tellurene: Novel group VI elemental 2D materials with nontrivial topological properties. 2D Mater., 2017, 4(4): 041003

[79] D. Ji , S. Cai , T. R. Paudel , H. Sun , C. Zhang , L. Han , Y. Wei , Y. Zang , M. Gu , Y. Zhang , W. Gao , H. Huyan , W. Guo , D. Wu , Z. Gu , E. Y. Tsymbal , P. Wang , Y. Nie , X. Pan . Freestanding crystalline oxide perovskites down to the monolayer limit. Nature, 2019, 570(7759): 87

[80] Y. Zhang , H. H. Ma , X. Gan , Y. Hui , Y. Zhang , J. Su , M. Yang , Z. Hu , J. Xiao , X. Lu , J. Zhang , Y. Hao . Emergent midgap excitons in large-size freestanding 2D strongly correlated perovskite oxide films. Adv. Opt. Mater., 2021, 9(10): 2100025

[81] Y. Lu , H. Zhang , Y. Wang , X. Zhu , W. Xiao , H. Xu , G. Li , Y. Li , D. Fan , H. Zeng , Z. Chen , X. Yang . Solar-driven interfacial evaporation accelerated electrocatalytic water splitting on 2D perovskite oxide/MXene heterostructure. Adv. Funct. Mater., 2023, 33(21): 2215061

[82] K. Burke . Perspective on density functional theory. J. Chem. Phys., 2012, 136(15): 150901

[83] N. Mounet , M. Gibertini , P. Schwaller , D. Campi , A. Merkys , A. Marrazzo , T. Sohier , I. E. Castelli , A. Cepellotti , G. Pizzi , N. Marzari . Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol., 2018, 13(3): 246

[84] A. K. Geim , I. V. Grigorieva . Van der Waals heterostructures. Nature, 2013, 499(7459): 419

[85] Y. Liu , N. O. Weiss , X. Duan , H. C. Cheng , Y. Huang , X. Duan . Van der Waals heterostructures and devices. Nat. Rev. Mater., 2016, 1(9): 16042

[86] K.NovoselovA.MishchenkoA.CarvalhoA.H. Castro Neto, 2D materials and van der Waals heterostructures, Science 353(6298), aac9439 (2016)

[87] A. Castellanos-Gomez , X. Duan , Z. Fei , H. R. Gutierrez , Y. Huang , X. Huang , J. Quereda , Q. Qian , E. Sutter , P. Sutter . Van der Waals heterostructures. Nat. Rev. Methods Primers, 2022, 2(1): 58

[88] X. L. Fan , R. F. Xin , L. Li , B. Zhang , C. Li , X. L. Zhou , H. Z. Chen , H. Y. Zhang , F. P. Ouyang , Y. Zhou . Progress in the preparation and physical properties of two-dimensional Cr-based chalcogenide materials and heterojunctions. Front. Phys., 2023, 19(2): 23401

[89] L. Deng , D. Yu . Deep learning: Methods and applications. Foundations and Trends in Signal Processing, 2014, 7(3-4): 197

[90] E. Moen , D. Bannon , T. Kudo , W. Graf , M. Covert , D. Van Valen . Deep learning for cellular image analysis. Nat. Methods, 2019, 16(12): 1233

[91] Y. LeCun , Y. Bengio , G. Hinton . Deep learning. Nature, 2015, 521(7553): 436

[92] L.DengG.HintonB.Kingsbury, New types of deep neural network learning for speech recognition and related applications: An overview, in: Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, May 26‒31, 2013, 2013

[93] D.W. OtterJ.R. MedinaJ.K. Kalita, A survey of the usages of deep learning for natural language processing, IEEE Trans. Neural Netw. Learn. Syst. 32(2), 604 (2021)

[94] M.Z. AlomT.M. TahaC.YakopcicS.WestbergP.SidikeM.S. NasrinM.HasanB.C. Van EssenA.A. S. AwwalV.K. Asari, A state-of-the-art survey on deep learning theory and architectures, Electronics (Basel) 8(3), 292 (2019)

[95] G. E. Hinton , R. R. Salakhutdinov . Reducing the dimensionality of data with neural networks. Science, 2006, 313(5786): 504

[96] M. I. Jordan , T. M. Mitchell . Machine learning: Trends, perspectives, and prospects. Science, 2015, 349(6245): 255

[97] W.S. McCullochW.Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5(4), 115 (1943)

[98] F. Rosenblatt . The perceptron: A probabilistic model for information storage and organization in the brain. Psychol. Rev., 1958, 65(6): 386

[99] D. E. Rumelhart , G. E. Hinton , R. J. Williams . Learning representations by back-propagating errors. Nature, 1986, 323(6088): 533

[100] K. Fukushima . Neocognitron: A hierarchical neural network capable of visual pattern recognition. Neural Netw., 1988, 1(2): 119

[101] Y. Lecun , L. Bottou , Y. Bengio , P. Haffner . Gradient-based learning applied to document recognition. Proc. IEEE, 1998, 86(11): 2278

[102] I. Goodfellow , J. Pouget-Abadie , M. Mirza , B. Xu , D. Warde-Farley , S. Ozair , A. Courville , Y. Bengio . Generative adversarial networks. Commun. ACM, 2020, 63(11): 139

[103] J.ChengY.YangX.Tang, ., Generative Adversarial Networks: A Literature Review, Trans. Internet Inf. Syst. (Seoul) 14(12) (2020)

[104] O.RonnebergerP.FischerT.Brox, U-net: Convolutional networks for biomedical image segmentation, in: Proceedings of the Medical Image Computing and Computer-Assisted Intervention-MICCAI 2015: 18th International Conference, Munich, Germany, October 5‒9, 2015, Proceedings, Part III 18, Springer, 2015

[105] H. Li , J. Wu , X. Huang , G. Lu , J. Yang , X. Lu , Q. Xiong , H. Zhang . Rapid and reliable thickness identification of two-dimensional nanosheets using optical microscopy. ACS Nano, 2013, 7(11): 10344

[106] H. C. Wang , S. W. Huang , J. M. Yang , G. H. Wu , Y. P. Hsieh , S. W. Feng , M. K. Lee , C. T. Kuo . Large-area few-layered graphene film determination by multispectral imaging microscopy. Nanoscale, 2015, 7(19): 9033

[107] Y. Li , N. Dong , S. Zhang , K. Wang , L. Zhang , J. Wang . Optical identification of layered MoS₂ via the characteristic matrix method. Nanoscale, 2016, 8(2): 1210

[108] J. Zhang , Y. Yu , P. Wang , C. Luo , X. Wu , Z. Sun , J. Wang , W. D. Hu , G. Shen . Characterization of atomic defects on the photoluminescence in two-dimensional materials using transmission electron microscope. InfoMat, 2019, 1(1): 85

[109] W. Zhao , B. Xia , L. Lin , X. Xiao , P. Liu , X. Lin , H. Peng , Y. Zhu , R. Yu , P. Lei , J. Wang , L. Zhang , Y. Xu , M. Zhao , L. Peng , Q. Li , W. Duan , Z. Liu , S. Fan , K. Jiang . Low-energy transmission electron diffraction and imaging of large-area graphene. Sci. Adv., 2017, 3(9): e1603231

[110] S. Yang . Scanning transmission electron microscopy (STEM) study on novel two-dimensional materials. Microsc. Microanal., 2020, 26(S2): 2372

[111] S. de Graaf , B. J. Kooi . Radiation damage and defect dynamics in 2D WS₂: A low-voltage scanning transmission electron microscopy study. 2D Mater., 2021, 9(1): 015009

[112] S. Kim , D. Moon , B. R. Jeon , J. Yeon , X. Li , S. Kim . Accurate atomic-scale imaging of two-dimensional lattices using atomic force microscopy in ambient conditions. Nanomaterials (Basel), 2022, 12(9): 1542

[113] D. S. Wastl , A. J. Weymouth , F. J. Giessibl . Atomically resolved graphitic surfaces in air by atomic force microscopy. ACS Nano, 2014, 8(5): 5233

[114] Q. Tu , B. Lange , Z. Parlak , J. M. J. Lopes , V. Blum , S. Zauscher . Quantitative subsurface atomic structure fingerprint for 2D materials and heterostructures by first-principles-calibrated contact-resonance atomic force microscopy. ACS Nano, 2016, 10(7): 6491

[115] C. Lee , H. Yan , L. E. Brus , T. F. Heinz , J. Hone , S. Ryu . Anomalous lattice vibrations of single- and few-layer MoS₂. ACS Nano, 2010, 4(5): 2695

[116] D. L. Silva , J. L. E. Campos , T. F. Fernandes , J. N. Rocha , L. R. P. Machado , E. M. Soares , D. R. Miquita , H. Miranda , C. Rabelo , O. P. Vilela Neto , A. Jorio , L. G. Cançado . Raman spectroscopy analysis of number of layers in mass-produced graphene flakes. Carbon, 2020, 161: 181

[117] I. Stenger , L. Schué , M. Boukhicha , B. Berini , B. Plaçais , A. Loiseau , J. Barjon . Low frequency Raman spectroscopy of few-atomic-layer thick hBN crystals. 2D Mater., 2017, 4(3): 031003

[118] Z. H. Ni , H. M. Wang , J. Kasim , H. M. Fan , T. Yu , Y. H. Wu , Y. P. Feng , Z. X. Shen . Graphene thickness determination using reflection and contrast spectroscopy. Nano Lett., 2007, 7(9): 2758

[119] R. Frisenda , Y. Niu , P. Gant , A. J. Molina-Mendoza , R. Schmidt , R. Bratschitsch , J. Liu , L. Fu , D. Dumcenco , A. Kis , D. P. De Lara , A. Castellanos-Gomez . Micro-reflectance and transmittance spectroscopy: a versatile and powerful tool to characterize 2D materials. J. Phys. D Appl. Phys., 2017, 50(7): 074002

[120] S. Y. Zeng , F. Li , C. Tan , L. Yang , Z. G. Wang . Defect repairing in two-dimensional transition metal dichalcogenides. Front. Phys., 2023, 18(5): 53604

[121] M. Ziatdinov , O. Dyck , A. Maksov , X. Li , X. Sang , K. Xiao , R. R. Unocic , R. Vasudevan , S. Jesse , S. V. Kalinin . Deep learning of atomically resolved scanning transmission electron microscopy images: Chemical identification and tracking local transformations. ACS Nano, 2017, 11(12): 12742

[122] J.MadsenP.LiuJ.KlingJ.B. WagnerT.W. HansenO.WintherJ.Schiøtz, A deep learning approach to identify local structures in atomic-resolution transmission electron microscopy images, Adv. Theory Simul. 1(8), 1800037 (2018)

[123] A. Maksov , O. Dyck , K. Wang , K. Xiao , D. B. Geohegan , B. G. Sumpter , R. K. Vasudevan , S. Jesse , S. V. Kalinin , M. Ziatdinov . Deep learning analysis of defect and phase evolution during electron beam-induced transformations in WS₂. npj Comput. Mater., 2019, 5(1): 12

[124] D. H. Yang , Y. S. Chu , O. F. N. Okello , S. Y. Seo , G. Moon , K. H. Kim , M. H. Jo , D. Shin , T. Mizoguchi , S. Yang , S. Y. Choi . Full automation of point defect detection in transition metal dichalcogenides through a dual mode deep learning algorithm. Mater. Horiz., 2024, 11(3): 747

[125] S. H. Yang , W. Choi , B. W. Cho , F. O. T. Agyapong-Fordjour , S. Park , S. J. Yun , H. J. Kim , Y. K. Han , Y. H. Lee , K. K. Kim , Y. M. Kim . Deep learning-assisted quantification of atomic dopants and defects in 2D materials. Adv. Sci. (Weinh.), 2021, 8(16): 2101099

[126] C. H. Lee , A. Khan , D. Luo , T. P. Santos , C. Shi , B. E. Janicek , S. Kang , W. Zhu , N. A. Sobh , A. Schleife , B. K. Clark , P. Y. Huang . Deep learning enabled strain mapping of single-atom defects in two-dimensional transition metal dichalcogenides with sub-picometer precision. Nano Lett., 2020, 20(5): 3369

[127] T.ChuL.ZhouB.ZhangF.Z. Xuan, Accurate atomic scanning transmission electron microscopy analysis enabled by deep learning, Nano Res., doi: 10.1007/s12274-023-6104-1 (2023)

[128] B.WuL.WangZ.Gao, A two-dimensional material recognition image algorithm based on deep learning, in: Proceedings of the 2019 International Conference on Information Technology and Computer Application (ITCA), IEEE, 2019

[129] Y. Saito , K. Shin , K. Terayama , S. Desai , M. Onga , Y. Nakagawa , Y. M. Itahashi , Y. Iwasa , M. Yamada , K. Tsuda . Deep-learning-based quality filtering of mechanically exfoliated 2D crystals. npj Computat. Mater., 2019, 5(1): 124

[130] B. Han , Y. Lin , Y. Yang , N. Mao , W. Li , H. Wang , K. Yasuda , X. Wang , V. Fatemi , L. Zhou , J. I. J. Wang , Q. Ma , Y. Cao , D. Rodan-Legrain , Y. Q. Bie , E. Navarro-Moratalla , D. Klein , D. MacNeill , S. Wu , H. Kitadai , X. Ling , P. Jarillo-Herrero , J. Kong , J. Yin , T. Palacios . Deep-learning-enabled fast optical identification and characterization of 2D materials. Adv. Mater., 2020, 32(29): 2000953

[131] S. Masubuchi , E. Watanabe , Y. Seo , S. Okazaki , T. Sasagawa , K. Watanabe , T. Taniguchi , T. Machida . Deep-learning-based image segmentation integrated with optical microscopy for automatically searching for two-dimensional materials. npj 2D Mater. Appl., 2020, 4(1): 3

[132] T.Y. LinM.MaireS.Belongie, ., Microsoft coco: Common objects in context, in: Proceedings of the Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6‒12, 2014, Proceedings, Part V 13, Springer, 2014

[133] S. Mahjoubi , F. Ye , Y. Bao , W. Meng , X. Zhang . Identification and classification of exfoliated graphene flakes from microscopy images using a hierarchical deep convolutional neural network. Eng. Appl. Artif. Intell., 2023, 119: 105743

[134] Y. Zhang , H. Zhang , S. Zhou , G. Liu , J. Zhu . Deep learning-based layer identification of 2D nanomaterials. Coatings, 2022, 12(10): 1551

[135] H.ZhaoJ.ShiX.Qi, ., Pyramid scene parsing network, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017

[136] X.QinZ.ZhangC.HuangM.DehghanO.R. ZaianeM.Jagersand, U²-net: Going deeper with nested U-structure for salient object detection, Pattern Recognit. 106, 107404 (2020)

[137] X. Dong , Y. Zhang , H. Li , Y. Yan , J. Li , J. Song , K. Wang , M. Jakobi , A. K. Yetisen , A. W. Koch . Microscopic image deblurring by a generative adversarial network for 2D nanomaterials: Implications for wafer-scale semiconductor characterization. ACS Appl. Nano Mater., 2022, 5(9): 12855

[138] L. Zhu , J. Tang , B. Li , T. Hou , Y. Zhu , J. Zhou , Z. Wang , X. Zhu , Z. Yao , X. Cui , K. Watanabe , T. Taniguchi , Y. Li , Z. V. Han , W. Zhou , Y. Huang , Z. Liu , J. C. Hone , Y. Hao . Artificial neuron networks enabled identification and characterizations of 2D materials and van der Waals heterostructures. ACS Nano, 2022, 16(2): 2721

[139] X. Dong , H. Li , K. Wang , B. Menze , M. Jakobi , A. K. Yetisen , A. W. Koch . Multispectral microscopic multiplexed (3M) imaging of atomically-thin crystals using deep learning. Adv. Opt. Mater., 2024, 12(2): 2300860

[140] G. A. Nemnes , T. L. Mitran , A. Manolescu . Gap prediction in hybrid graphene-hexagonal boron nitride nanoflakes using artificial neural networks. J. Nanomater., 2019, 2019: 6960787

[141] Y. Dong , C. Wu , C. Zhang , Y. Liu , J. Cheng , J. Lin . Bandgap prediction by deep learning in configurationally hybridized graphene and boron nitride. npj Comput. Mater., 2019, 5(1): 26

[142] C. Cortes , V. Vapnik . Support-vector networks. Mach. Learn., 1995, 20(3): 273

[143] Y. Ma , S. Lu , Y. Zhang , T. Zhang , Q. Zhou , J. Wang . Accurate energy prediction of large-scale defective two-dimensional materials via deep learning. Appl. Phys. Lett., 2022, 120(21): 213103

[144] M. Dewapriya , R. Rajapakse , W. Dias . Characterizing fracture stress of defective graphene samples using shallow and deep artificial neural networks. Carbon, 2020, 163: 425

[145] Y. C. Hsu , C. H. Yu , M. J. Buehler . Using deep learning to predict fracture patterns in crystalline solids. Matter, 2020, 3(1): 197

[146] A. J Lew , C. H. Yu , Y. C. Hsu , M. J. Buehler . Deep learning model to predict fracture mechanisms of grapheme. npj 2D Mater. Appl., 2021, 5(1): 48

[147] T. Zhang , X. Li , S. Kadkhodaei , H. Gao . Flaw insensitive fracture in nanocrystalline graphene. Nano Lett., 2012, 12(9): 4605

[148] C. H. Yu , C. Y. Wu , M. J. Buehler . Deep learning based design of porous graphene for enhanced mechanical resilience. Comput. Mater. Sci., 2022, 206: 111270

[149] M.S. ElapoluM.I. R. ShishirA.Tabarraei, A novel approach for studying crack propagation in polycrystalline graphene using machine learning algorithms, Comput. Mater. Sci. 201, 110878 (2022)

[150] M. S. Elapolu , A. Tabarraei . Mechanical and fracture properties of polycrystalline graphene with hydrogenated grain boundaries. J. Phys. Chem. C, 2021, 125(20): 11147

[151] A. Shekhawat , R. O. Ritchie . Toughness and strength of nanocrystalline graphene. Nat. Commun., 2016, 7(1): 10546

[152] M. I. R. Shishir , A. Tabarraei . Traction–separation laws of graphene grain boundaries. Phys. Chem. Chem. Phys., 2021, 23(26): 14284

[153] M.I. R. ShishirM.S. R. ElapoluA.Tabarraei, A deep learning model for predicting mechanical properties of polycrystalline graphene, Comput. Mater. Sci. 218, 111924 (2023)

[154] Y. Shen , S. Zhu . Machine learning mechanical properties of defect-engineered hexagonal boron nitride. Comput. Mater. Sci., 2023, 220: 112030

[155] H. Yang , Z. Zhang , J. Zhang , X. C. Zeng . Machine learning and artificial neural network prediction of interfacial thermal resistance between graphene and hexagonal boron nitride. Nanoscale, 2018, 10(40): 19092

[156] J. Wan , J. W. Jiang , H. S. Park . Machine learning-based design of porous graphene with low thermal conductivity. Carbon, 2020, 157: 262

[157] Q. Liu , Y. Gao , B. Xu . Transferable, deep-learning-driven fast prediction and design of thermal transport in mechanically stretched graphene flakes. ACS Nano, 2021, 15(10): 16597

[158] X. Zhang , A. Chen , Z. Zhou . High-throughput computational screening of layered and two-dimensional materials. Wiley Interdiscip. Rev. Comput. Mol. Sci., 2019, 9(1): e1385

[159] V. Wang , G. Tang , Y. C. Liu , R. T. Wang , H. Mizuseki , Y. Kawazoe , J. Nara , W. T. Geng . High-throughput computational screening of two-dimensional semiconductors. J. Phys. Chem. Lett., 2022, 13(50): 11581

[160] S. Sarikurt , T. Kocabaş , C. Sevik . High-throughput computational screening of 2D materials for thermoelectrics. J. Mater. Chem. A, 2020, 8(37): 19674

[161] E. O. Pyzer-Knapp , C. Suh , R. Gómez-Bombarelli , J. Aguilera-Iparraguirre , A. Aspuru-Guzik . What is high-throughput virtual screening? A perspective from organic materials discovery. Annu. Rev. Mater. Res., 2015, 45(1): 195

[162] X. Y. Ma , J. P. Lewis , Q. B. Yan , G. Su . Accelerated discovery of two-dimensional optoelectronic octahedral oxyhalides via high-throughput ab initio calculations and machine learning. J. Phys. Chem. Lett., 2019, 10(21): 6734

[163] C. G. Van de Walle , J. Neugebauer . First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys., 2004, 95(8): 3851

[164] B. K. Shoichet . Virtual screening of chemical libraries. Nature, 2004, 432(7019): 862

[165] S. Ghosh , A. Nie , J. An , Z. Huang . Structure-based virtual screening of chemical libraries for drug discovery. Curr. Opin. Chem. Biol., 2006, 10(3): 194

[166] M. Foscato , G. Occhipinti , V. Venkatraman , B. K. Alsberg , V. R. Jensen . Automated design of realistic organometallic molecules from fragments. J. Chem. Inf. Model., 2014, 54(3): 767

[167] H. Mauser , M. Stahl . Chemical fragment spaces for de novo design. J. Chem. Inf. Model., 2007, 47(2): 318

[168] G. R. Schleder , A. C. Padilha , C. M. Acosta , M. Costa , A. Fazzio . From DFT to machine learning: recent approaches to materials science – A review. J. Phys.: Mater., 2019, 2(3): 032001

[169] Y. Dong , D. Li , C. Zhang , C. Wu , H. Wang , M. Xin , J. Cheng , J. Lin . Inverse design of two-dimensional graphene/h-BN hybrids by a regressional and conditional GAN. Carbon, 2020, 169: 9

[170] V. Fung , J. Zhang , G. Hu , P. Ganesh , B. G. Sumpter . Inverse design of two-dimensional materials with invertible neural networks. npj Computat. Mater., 2021, 7(1): 200

[171] S. Wu , Z. Wang , H. Zhang , J. Cai , J. Li . Deep learning accelerates the discovery of two-dimensional catalysts for hydrogen evolution reaction. Energy & Environm. Mater., 2023, 6(1): e12259

[172] S. S. Chong , Y. S. Ng , H. Q. Wang , J. C. Zheng . Advances of machine learning in materials science: Ideas and techniques. Front. Phys., 2024, 19(1): 13501

[173] B. Ryu , L. Wang , H. Pu , M. K. Y. Chan , J. Chen . Understanding, discovery, and synthesis of 2D materials enabled by machine learning. Chem. Soc. Rev., 2022, 51(6): 1899

[174] H. Yin , Z. Sun , Z. Wang , D. Tang , C. H. Pang , X. Yu , A. S. Barnard , H. Zhao , Z. Yin . The data-intensive scientific revolution occurring where two-dimensional materials meet machine learning. Cell Rep. Phys. Sci., 2021, 2(7): 100482

[175] Z.SiD.ZhouJ.YangX.Lin, 2D material property characterizations by machine-learning-assisted microscopies, Appl. Phys. A 129(4), 248 (2023)

Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

The authors gratefully acknowledge support from the National Key Research and Development Program of China (Grant No. 2022YFA1404201), the National Natural Science Foundation of China (Nos. U22A2091, 62222509, 62127817, 62075120, 62075122, 62205187, 62105193, and 6191101445), Shanxi Province Science and Technology Innovation Talent Team (No. 202204051001014), the Science and Technology Cooperation Project of Shanxi Province (No. 202104041101021), the Key Research and Development Project of Shanxi Province (No. 202102030201007), and 111 Projects (Grant No. D18001).

RIGHTS & PERMISSIONS

2024 The Authors