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

doi:10.1007/s11467-024-1394-7

Front. Phys.

2024, Vol. 19

Issue (5) : 53601 https://doi.org/10.1007/s11467-024-1394-7

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

Xinqin Meng¹, Chengbing Qin^1,²(

), Xilong Liang³, Guofeng Zhang¹, Ruiyun Chen¹, Jianyong Hu¹, Zhichun Yang¹, Jianzhong Huo³, Liantuan Xiao^1,²(

), Suotang Jia¹

¹. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
². College of Physics, Taiyuan University of Technology, Taiyuan 030024, China
³. Taiyuan Central Hospital of Shanxi Medical University, Taiyuan 030009, China

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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.

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

Corresponding Author(s): Chengbing Qin,Liantuan Xiao

About author: Li Liu and Yanqing Liu contributed equally to this work.

Issue Date: 15 April 2024

Cite this article:

Xinqin Meng,Chengbing Qin,Xilong Liang, et al. Deep learning in two-dimensional materials: Characterization, prediction, and design[J]. Front. Phys. , 2024, 19(5): 53601.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1394-7
https://academic.hep.com.cn/fop/EN/Y2024/V19/I5/53601

Fig.1 The taxonomy of artificial intelligence (AI) and diagram of the structure of a commonly used neural network. (a) The taxonomy of AI, where ML represents machine learning, SNN represents the spiking neural network, NN represents the neural network, and DL represents deep learning. (b) The overall architecture of CNN. (c) GAN model frame diagram. (d) U-net architecture. (a, b) Reproduced with permission from Ref. [94]. (c) Reproduced with permission from Ref. [103]. (d) Reproduced with permission from Ref. [104].

Fig.2 Defects identification of 2D materials based on the deep learning methods. (a) The schematic architecture of FCN with encoder?decoder structure. (b) Using FCN and Laplacian of Gaussian blob detection method to obtain atomic positions from raw experimental data on graphene. Imaging area: 2.16 nm × 2.16 nm. (c) Left: The first frame from STEM movie on Mo-doped WS₂ as a training image. Middle: The outcome derived from the application of Fourier transform and high-pass filtering to the left image. Right: The ultimate thresholded difference image serves as ground truth. (d) Gaussian mixture model clusters the defects into five categories. From left to right represents categories 1 to 5. (e) The upper part exhibits ADF STEM images of WSe₂ with V dopant under electron beam irradiation. The lower part presents the corresponding atom-site classification maps, acquired through the established deep learning algorithm. (a, b) Reproduced with permission from Ref. [121]. (c, d) Reproduced with permission from Ref. [123]. (e) Reproduced with permission from Ref. [125].

Fig.3 Materials identification and thickness analysis of 2D materials based on the deep learning methods. (a) Process of quality filtering of 2D crystals via deep-neural network. (b) OM images of 13 materials. (c) Schematic diagram of the structure of 2DMOINet. (d) The label map predicted by 2DMOINet segments individual 2D material flakes and provides labels for their material identities and thickness. (e) Using improved U-net to identify the number of layers for both out-of-focus images and refocused images, respectively. Scale bar: 100 μm. (f) The OM images of the heterostructures. (g) Raman mapping of the heterostructures in (f). Left: The peak intensity mapping of

E 2 g 1

mode in WS₂. Right: The peak intensity mapping of

E 2 g 1

mode in MoS₂. (h) Predictions from ANN for heterostructures in (f). (i) The OM images of the graphene. (j) Predictions from the model based on Mask-RCNN for graphene in (i). The segmentation masks are shown in color, and the category and confidence are also indicated. (a) Reproduced with permission from Ref. [129]. (b?d) Reproduced with permission from Ref. [130]. (e) Reproduced with permission from Ref. [137]. (f?h) Reproduced with permission from Ref. [138]. (i, j) Reproduced with permission from Ref. [131].

Fig.4 Prediction of electronic properties of graphene and related materials based on the deep learning methods. (a) A hybrid h-BN graphene nanoflake. (b, c) Results from the first ANN model and the second ANN model, represented by blue and red for the training and testing sets, respectively. (d, e) Prediction performance of four models. (d) The predictive bandgap error of the four models in 4 × 4 supercell systems. (e) The comparison between the predicted bandgap generated by the four models and the bandgap calculated by DFT. (f) Data preparation. Large amounts of data are randomly generated under limited conditions. (g) The prediction results of CNN for different defect combinations at varying defect distances. (a?c) Reproduced with permission from Ref. [140]. (d, e) Reproduced with permission from Ref. [141]. (f, g) Reproduced with permission from Ref. [143].

Fig.5 Prediction of mechanical properties of 2D materials based on the deep learning methods. (a) Schematic diagram of the model based on ConvLSTM. (b) Comparison between the predicted results from ConvLSTM-based model on the test set and the MD simulation results. (c) The input and output images in the dataset. (d) Crack length comparison from MD simulation and the model based on CNN and Bi-RNNs. (e) The relationship between crack length and grain size plots from MD simulation and the model. (f) The deep CNN model is employed to extract the average grain size of polycrystalline graphene, demonstrating its testing performance. (g) The standard deviation of fracture stress and Young’s modulus with grain size distribution obtained by MD simulation. (a, b) Reproduced with permission from Ref. [146]. (c?e) Reproduced with permission from Ref. [149]. (f, g) Reproduced with permission from Ref. [153].

Fig.6 Prediction of thermal conductivity of 2D materials based on the deep learning methods. Machine learning results of (a) linear regression, (b) 2^nd order polynomial regression, (c) decision tree, and (d) random forest algorithms. The red and black squares represent the machine learning predicted values and the target interfacial thermal resistance values, respectively. (e?h) Predictive results of ANN with different architectures: (e) with one hidden layer, each layer containing 10 neurons; (f) with one hidden layer, each layer containing 20 neurons; (g) with two hidden layers, each layer containing 10 neurons; (h) with two hidden layers, each layer containing 20 neurons. The red and black squares represent the ANN predicted values and the target interfacial thermal resistance values, respectively. (i) The structure of porous graphene. The atomic clusters in the central region (highlighted in blue) are candidate positions for generating holes. (j) Exploded schematic of piled graphene with dimensions l × w. (k) The process of generating fingerprints for piled graphene structures. (l) A databank consisting of geometric features and thermal conductivity of piled graphene structures. (a?h) Reproduced with permission from Ref. [155]. (i) Reproduced with permission from Ref. [156]. (j?l) Reproduced with permission from Ref. [157].

Fig.7 2D materials design based on deep learning methods. (a) The four science paradigms: empirical, theoretical, computational, and data-driven. (b) The architecture of RCGAN used for the design of 2D graphene and h-BN hybrids with specific bandgap. (c) For the 4 × 4 supercell systems, the comparison between the bandgap of the generated structure and the desired bandgap, with a correlation factor of 0.87. (d) For the 4 × 4 supercell system, the distribution of bandgap errors for the generated structures with a mean absolute error of 9.45%. (e) MoS₂ model and design parameter space. (f) Using DFT calculations to validate the performance of candidate structures generated by the MatDesINNe-cINN model. For candidate structures with a target bandgap of 0.5 eV generated by the model, the average absolute error is 0.111 eV. (g) The MoS₂ example structure generated by the MatDesINNe-cINN model with a bandgap value of 0.5 eV. (h) Time required to calculate hydrogen evolution reaction adsorption energies of 34 materials. (a) Reproduced with permission from Ref. [168]. (b?d) Reproduced with permission from Ref. [169]. (e?g) Reproduced with permission from Ref. [170]. (h) Reproduced with permission from Ref. [171].

Research area	2D materials	Model	Data sources	Applications	Ref.

Structure characterization	graphene, Mo_1–xW_xSe₂	FCN	simulated images	defects identification	[121]
	graphene, metallic nanoparticles	CNN	simulated images using multislice algorithm	recognition and classification of atomic structures	[122]
	Mo-doped WS₂	CNN with encoder–decoder structure	experimental STEM images	defects identification	[123]
	2H-MoTe₂	CNN	simulated STEM images	point defects identification	[124]
	TMDs	CNN, U-net	simulated ADF STEM images using multislice algorithm	quantification of dopants and defects	[125]
	WSe_2–2xTe_2x	FCN	simulated images using Computem	localization and classification of point defects	[126]
	Ti₃C₂T_x	FCN	simulated images and experimental STEM images	defects and atoms identification	[127]
		SegNet	OM images	materials identification	[128]
	graphene, MoS₂	U-net	OM images	thickness characterization	[129]
	13 typical 2D materials	2DMOINet model based on encoder–decoder structure	OM images	materials identification and thickness characterization	[130]
	graphene, h-BN, MoS₂, WTe₂	Mask-RCNN	OM images	materials identification and thickness characterization	[131]
	graphene	Deep-CNN	OM images	materials identification and thickness characterization	[133]
	graphene, MoS₂	U²-net	OM images from [129]	thickness characterization	[134]
	MoS₂	GAN, U-net	OM images	deblurring and thickness characterization	[137]
	WS₂, h-BN, MoS₂, MoTe₂, WSe₂, BSCCO, MoSe₂, graphene	ANN	OM images (RGB/HSV)	materials identification, thickness characterization and identification defect concentrations	[138]
	MoS₂	GAN, U-net	multispectral images	deblurring and thickness characterization	[139]
Properties prediction	hybrid graphene-h-BN	ANN	DFT calculation	bandgap	[140]
	hybrid graphene-h-BN	CNN	DFT calculation	bandgap	[141]
	defected graphene, MoS₂	CNN	DFT calculation	formation energy	[143]
	defected graphene	ANN, CNN	MD simulation	fracture stress	[144]
	graphene	ConvLSTM network	MD simulation	fracture path	[146]
	polycrystalline graphene	CNN, Bi-RNN	MD simulation	fracture path	[149]
	polycrystalline graphene	Deep-CNN	MD simulation	Young’s modulus and fracture stress	[153]
	h-BN	Deep-CNN	MD simulation	Young’s modulus and tensile strength	[154]
	graphene, h-BN	ANN	MD simulation	interfacial thermal resistance	[155]
	porous graphene	CNN	MD simulation	thermal conductivity	[156]
	mechanically stretched graphene	DNN	MD simulation	thermal conductivity	[157]
Material design	hybrids graphene/h-BN	GAN	DFT calculation	generate graphene/h-BN hybrids with specific bandgap	[169]
	MoS₂	INN	DFT calculation	generate MoS₂ with specific bandgap	[170]
	porous graphene	CNN	MD simulation	find porous graphene with low thermal conductivity	[156]
	2D material catalysts	CGCNN	DFT calculation	find high-performance hydrogen evolution reaction catalysts	[171]

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