检索结果-内蒙古大学图书馆

An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Dai, Xiaoying Zhou, Aihui Zhou, Yuzhi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle (∼ 1.05◦). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations. © 2023, CC BY.

关键词： Electronic structure

A Greedy Sensor Selection Algorithm for Hyperparameterized Linear Bayesian Inverse Problems

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Aretz, Nicole Chen, Peng Degen, Denise D. Veroy, Karen Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th St AustinTX78712 United States School of Computational Science and Engineering Georgia Institute of Technology 756 W Peachtree St NW AtlantaGA30308 United States Computational Geoscience Geothermics and Reservoir Geophysics RWTH Aachen University Mathieustr. 30 Aachen52074 Germany Center for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven5612 AZ Netherlands

We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed physical system. To optimally reduce the uncertainty in the system’s model with a single set of sensors, the initial sensor placement needs to account for the non-linear state changes of all admissible configurations. We address this requirement through an observability coefficient which links the posteriors’ uncertainties directly to the choice of sensors. We propose a greedy sensor selection algorithm to iteratively improve the observability coefficient for all configurations through orthogonal matching pursuit. The algorithm allows explicitly correlated noise models even for large sets of candidate sensors, and remains computationally efficient for high-dimensional forward models through model order reduction. We demonstrate our approach on a large-scale geophysical model of the Perth Basin, and provide numerical studies regarding optimality and scalability with regard to classic optimal experimental design utility functions. © 2023, CC BY.

关键词： Inverse problems

Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Wang, Ting Zhou, Yuzhi Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for the effective potentials of the incommensurate systems and utilize that, the localization of the electron density can be inferred from the effective potentials. Moreover, we show that the spectrum distribution can also be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectrum distribution of the systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Elastic waves

A Unified Framework for Exploratory Learning-Aided Community Detection Under Topological Uncertainty

学校读者我要写书评

暂无评论

IEEE Transactions on Network science and engineering 2025年

作者： Hou, Yu Tran, Cong Li, Ming Shin, Won-Yong Yonsei University School of Mathematics and Computing Computational Science and Engineering Seoul03722 Korea Republic of Posts and Telecommunications Institute of Technology Faculty of Information Technology Hanoi100000 Viet Nam Zhejiang Institute of Optoelectronics Jinhua321004 China Zhejiang Normal University Zhejiang Key Laboratory of Intelligent Education Technology and Application Jinhua321004 China Graduate School of Artificial Intelligence Pohang37673 Korea Republic of

In social networks, the discovery of community structures has received considerable attention as a fundamental problem in various network analysis tasks. However, due to privacy concerns or access restrictions, the network structure is often uncertain, thereby rendering established community detection approaches ineffective without costly network topology acquisition. To tackle this challenge, we present META-CODE, a unified framework for detecting overlapping communities via exploratory learning aided by easy-to-collect node metadata when networks are topologically unknown (or only partially known). Specifically, META-CODE consists of three iterative steps in addition to the initial network inference step: 1) node-level community-affiliation embeddings based on graph neural networks (GNNs) trained by our new reconstruction loss, 2) network exploration via community-affiliation-based node queries, and 3) network inference using an edge connectivity-based Siamese neural network model from the explored network. Through extensive experiments on three real-world datasets including two large networks, we demonstrate: (a) the superiority of META-CODE over benchmark community detection methods, achieving remarkable gains up to 65.55% on the Facebook dataset over the best competitor among our selected competitive methods in terms of normalized mutual information (NMI), (b) the impact of each module in META-CODE, (c) the effectiveness of node queries in META-CODE based on empirical evaluations and theoretical findings, and (d) the convergence of the inferred network. © 2013 IEEE.

关键词： Structured Query Language

A Survey of Recent Advances in Optimization Methods for Wireless Communications

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Liu, Ya-Feng Chang, Tsung-Hui Hong, Mingyi Wu, Zheyu So, Anthony Man-Cho Jorswieck, Eduard A. Yu, Wei The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Science and Engineering The Chinese University of Hong Kong Shenzhen Shenzhen China Shenzhen Research Institute of Big Data China The Department of Electrical and Computer Engineering University of Minnesota MinneapolisMN55455 United States The Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong The Institute for Communication Technology Technische Universitat Braunschweig Germany The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada

Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless communication and networking technologies from 1G to 5G and onto the future 6G, the innovations in wireless technologies have also substantially transformed the nature of the underlying mathematical optimization problems upon which the system designs are based and have sparked significant innovations in the development of methodologies to understand, to analyze, and to solve those problems. In this paper, we provide a comprehensive survey of recent advances in mathematical optimization theory and algorithms for wireless communication system design. We begin by illustrating common features of mathematical optimization problems arising in wireless communication system design. We discuss various scenarios and use cases and their associated mathematical structures from an optimization perspective. We then provide an overview of recently developed optimization techniques in areas ranging from nonconvex optimization, global optimization, and integer programming, to distributed optimization and learning-based optimization. The key to successful solution of mathematical optimization problems is in carefully choosing or developing suitable algorithms (or neural network architectures) that can exploit the underlying problem structure. We conclude the paper by identifying several open research challenges and outlining future research directions. Copyright © 2024, The Authors. All rights reserved.

关键词： Beamforming

A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Sky, Adam Neunteufel, Michael Hale, Jack S. Zilian, Andreas Institute of Computational Engineering and Sciences Department of Engineering Faculty of Science Technology and Medicine University of Luxembourg 6 Avenue de la Fonte Esch-sur-AlzetteL-4362 Luxembourg Institute of Analysis and Scientific Computing Technische Universität Wien Wiedner Hauptstr. 8-10 Wien1040 Austria

In this work we develop new finite element discretisations of the shear-deformable Reissner-Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence M ∈ HZ ⊂ Hsym(Div). The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the discontinuous Lebesgue space φ ∈ [L2]2, such that the Kirchhoff-Love constraint can be satisfied for t → 0. In order to preserve optimal convergence rates across all variables for the case t → 0, we present an extension of the formulation using Raviart-Thomas elements for the shear stress q ∈ RT ⊂ H(div). We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shearlocking, curved geometries and an L-shaped domain with a singularity in the bending moments M. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods. © 2023, CC BY-NC-ND.

关键词： Mindlin plates

A New Adaptive Balanced Augmented Lagrangian Method with Application to ISAC Beamforming Design

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Wu, Jiageng Jiang, Bo Li, Xinxin Liu, Ya-Feng Yuan, Jianhua School of Mathematics Jilin University Changchun130012 China Ministry of Education Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Sciences Beijing University of Posts and Telecommunications Beijing100876 China

In this paper, we consider a class of convex programming problems with linear equality constraints, which finds broad applications in machine learning and signal processing. We propose a new adaptive balanced augmented Lagrangian (ABAL) method for solving these problems. The proposed ABAL method adaptively selects the stepsize parameter and enjoys a low per-iteration complexity, involving only the computation of a proximal mapping of the objective function and the solution of a linear equation. These features make the proposed method wellsuited to large-scale problems. We then custom-apply the ABAL method to solve the ISAC beamforming design problem, which is formulated as a nonlinear semidefinite program in a previous work. This customized application requires careful exploitation of the problem's special structure such as the property that all of its signal-to-interference-and-noise-ratio (SINR) constraints hold with equality at the solution and an efficient computation of the proximal mapping of the objective function. Simulation results demonstrate the efficiency of the proposed ABAL method. © 2024, CC BY.

关键词： Signal to noise ratio

A BROKEN HARDY INEQUALITY ON FINITE ELEMENT SPACE AND APPLICATION TO STRAIN GRADIENT ELASTICITY

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Liao, Yulei Ming, Pingbing Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore119076 Singapore LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical analysis for the strain gradient elasticity with natural boundary conditions. A mixed finite element pair is employed to solve this model with nearly incompressible materials. This pair is quasi-stable with a logarithmic factor, which is not significant in the approximation error, and converges robustly in the incompressible limit and uniformly in the microscopic material parameter. Numerical results back up that the theoretical predictions are nearly optimal. Moreover, the regularity estimates for the model over a smooth domain have been proved with the aid of the Agmon-Douglis-Nirenberg theory. Copyright © 2025, The Authors. All rights reserved.

关键词： Set theory

FINITE CONVERGENCE OF MOMENT-SOS RELAXATIONS WITH NON-REAL RADICAL IDEALS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Huang, Lei Nie, Jiawang Yuan, Ya-Xiang Department of Mathematics University of California 9500 Gilman Drive La Jolla San DiegoCA92093 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100049 China

We consider the linear conic optimization problem with the cone of nonnegative polynomials. Its dual optimization problem is the generalized moment problem. Moment-SOS relaxations are powerful for solving them. This paper studies finite convergence of the Moment-SOS hierarchy when the constraining set is defined by equations whose ideal may not be real radical. Under the archimedeanness, we show that the Moment-SOS hierarchy has finite convergence if some classical optimality conditions hold at every minimizer of the optimal nonnegative polynomial for the linear conic optimization problem. When the archimedeanness fails (this is the case for unbounded sets), we propose a homogenized Moment-SOS hierarchy and prove its finite convergence under similar assumptions. Furthermore, we also prove the finite convergence of the Moment-SOS hierarchy with denominators. In particular, this paper resolves a conjecture posed in the earlier work. Copyright © 2023, The Authors. All rights reserved.

关键词： Polynomials