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 chal...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 highprecision 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.展开更多
In this paper, we consider the generalized variational inequality GVI（F, g, C）, where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We propose two iter...In this paper, we consider the generalized variational inequality GVI（F, g, C）, where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We propose two iterative algorithms to find approximate solutions of the GVI（F,g, C）. Strong convergence results are established and applications to constrained generalized pseudo-inverse are included.展开更多
基金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)+3 种基金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)111 Projects(Grant No.D18001).
文摘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 highprecision 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.
文摘In this paper, we consider the generalized variational inequality GVI（F, g, C）, where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We propose two iterative algorithms to find approximate solutions of the GVI（F,g, C）. Strong convergence results are established and applications to constrained generalized pseudo-inverse are included.
