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Mathematical and numerical study of an inverse source problem for the biharmonic wave equation

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arXiv 2023年

作者： Chang, Yan Guo, Yukun Yin, Tao Zhao, Yue School of Mathematics Harbin Institute of Technology Harbin China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematics and Statistics Central China Normal University Wuhan China

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into a radiating source and a non-radiating source. The radiating source can be uniquely determined by Dirichlet boundary measurements at a fixed wavenumber. Moreover, we derive a Lipschitz stability estimate for determining the radiating source. On the other hand, the non-radiating source does not produce any scattered fields outside the support of the source function. Numerically, we propose a novel source reconstruction method based on Fourier series expansion by multi-wavenumber boundary measurements. Numerical experiments are presented to verify the accuracy and efficiency of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Wave equations

Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations

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Science China mathematics 2020年第1期63卷 39-60页

作者： Mohammed Harunor Rashid Ya-xiang Yuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Faculty of ScienceUniversity of Rajshahi 6205Bangladesh

Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:U→Y is a nonsmooth function and F:X■Y is a set-valued mapping with closed *** introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this ***,under the point-based approximation of f on U and metrically regular property of f+F,we present quadratic rate of convergence of this ***,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+F is metrically *** example of nonsmooth functions that have p-point-based approximation is ***,a numerical experiment is given which illustrates the theoretical result.

关键词： set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation

A riemannian exponential augmented lagrangian method for computing the projection robust Wasserstein distance 23

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A riemannian exponential augmented lagrangian method for com...

Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Bo Jiang Ya-Feng Liu Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing 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 Beijing China

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the step-sizes in efforts as done in the existing methods. We show that iRBBS can return an ε-stationary point of the original PRW distance problem within O(ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance.

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Quantized Constant-Envelope Waveform Design for Massive MIMO DFRC Systems

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arXiv 2024年

作者： Wu, Zheyu Liu, Ya-Feng Chen, Wei-Kun Masouros, Christos 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 Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The Department of Electronic and Electrical Engineering University College London Torrington Place LondonWC1E 7JE United Kingdom

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances. Copyright © 2024, The Authors. All rights reserved.

关键词： Mean square error

An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

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arXiv 2023年

作者： Chen, Wei-Kun Wu, Zheyu Zhang, Rui-Jin Liu, Ya-Feng Dai, Yu-Hong Luo, Zhi-Quan The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China 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 Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined;and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality. Copyright © 2023, The Authors. All rights reserved.

关键词： Resource allocation

ADAPTIVE IMPORTANCE SAMPLING FOR DEEP RITZ

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arXiv 2023年

作者： Wan, Xiaoliang Zhou, Tao Zhou, Yuancheng Department of Mathematics Center for Computation and Technology Louisiana State University Baton Rouge70803 United States LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

We introduce an adaptive sampling method for the Deep Ritz method aimed at solving partial differential equations(PDEs). Two deep neural networks are used. One network is employed to approximate the solution of PDEs, while the other one is a deep generative model used to generate new collocation points to refine the training set. The adaptive sampling procedure consists of two main steps. The first step is solving the PDEs using the Deep Ritz method by minimizing an associated variational loss discretized by the collocation points in the training set. The second step involves generating a new training set, which is then used in subsequent computations to further improve the accuracy of the current approximate solution. We treat the integrand in the variational loss as an unnormalized probability density function(PDF) and approximate it using a deep generative model called bounded KRnet. The new samples and their associated PDF values are obtained from the bounded KRnet. With these new samples and their associated PDF values, the variational loss can be approximated more accurately by importance sampling. Compared to the original Deep Ritz method, the proposed adaptive method improves accuracy, especially for problems characterized by low regularity and high dimensionality. We demonstrate the effectiveness of our new method through a series of numerical experiments. © 2023, CC BY.

关键词： Importance sampling

A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model

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arXiv 2024年

作者： Liao, Hong-Lin Tang, Tao Wang, Xuping Zhou, Tao School of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China MIIT Nanjing211106 China School of Electrical and Computer Engineering Guangzhou Nanfang College Institute for Advanced Study BNU-HKBU United International College China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity assumption of nonlinear bulk. With the help of discrete orthogonal convolution kernels, an updated time-space splitting technique is developed to establish the uniform boundedness of stage solutions for a refined class of IERK methods in which the associated differentiation matrices and the average dissipation rates are always independent of the time-space discretization meshes. This makes the refined IERK methods highly advantageous in self-adaptive time-stepping procedures as some larger adaptive step-sizes in actual simulations become possible. From the perspective of optimizing the average dissipation rate, we construct some parameterized refined IERK methods up to third-order accuracy, in which the involved diagonally implicit Runge-Kutta methods for the implicit part have an explicit first stage and allow a stage-order of two such that they are not necessarily algebraically stable. Then we are able to establish, for the first time, the original energy dissipation law and the unconditional L2 norm convergence. Extensive numerical tests are presented to support our *** Codes 35K58, 65L20, 65M06, 65M12 © 2024, CC BY-NC-ND.

关键词： Runge Kutta methods

DFD-Net:lung cancer detection from denoised CT scan image using deep learning

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Frontiers of Computer Science 2021年第2期15卷 119-131页

作者： Worku J.SORI Jiang FENG Arero W.GODANA Shaohui LIU Demissie J.GELMECHA School of Electrical Engineering and Computing Department of Computer Science and EngineeringAdama Science and Technology UniversityAdama1888Ethiopia Faculty of Natural Computational Science Department of Mathematics Bule Hora UniversityBule HoraHagere Maryam144Ethiopia School of Computer Science and Technology Harbin Institute of TechnologyHarbin150001China Peng Cheng Laboratory Shenzhen518052China School of Electrical Engineering and Computing Department of Electronics and Communications EngineeringAdama Science and Technology UniversityAdama1888Ethiopia

The availability of pulmonary nodules in CT scan image of lung does not completely specify *** noise in an image and morphology of nodules,like shape and size has an implicit and complex association with cancer,and thus,a careful analysis should be mandatory on every suspected nodules and the combination of information of every *** this paper,we introduce a“denoising first”two-path convolutional neural network(DFD-Net)to address this *** introduced model is composed of denoising and detection part in an end to end ***,a residual learning denoising model(DR-Net)is employed to remove noise during the preprocessing ***,a two-path convolutional neural network which takes the denoised image by DR-Net as an input to detect lung cancer is *** two paths focus on the joint integration of local and global *** this end,each path employs different receptive field size which aids to model local and global *** further polish our model performance,in different way from the conventional feature concatenation approaches which directly concatenate two sets of features from different CNN layers,we introduce discriminant correlation analysis to concatenate more representative ***,we also propose a retraining technique that allows us to overcome difficulties associated to the image labels *** found that this type of model easily first reduce noise in an image,balances the receptive field size effect,affords more representative features,and easily adaptable to the inconsistency among nodule shape and *** intensive experimental results achieved competitive results.

关键词： medical image discriminant correlation analysis features fusion image detection denoising

Mixing between flavor singlets in lattice gauge theories coupled to matter fields in multiple representations

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Physical Review D 2024年第7期110卷 074504页

作者： Ed Bennett Niccolò Forzano Deog Ki Hong Ho Hsiao Jong-Wan Lee C.-J. David Lin Biagio Lucini Maurizio Piai Davide Vadacchino Fabian Zierler Swansea Academy of Advanced Computing Department of Physics Faculty of Science and Engineering Department of Physics Extreme Physics Institute Institute of Physics Particle Theory and Cosmology Group Center for Theoretical Physics of the Universe Centre for Theoretical and Computational Physics Centre for High Energy Physics Department of Mathematics Faculty of Science and Engineering Centre for Mathematical Sciences

We provide the first extensive, numerical study of the nontrivial problem of mixing between flavor-singlet composite states emerging in strongly coupled lattice field theories with matter field content consisting of fermions transforming in different representations of the gauge group. The theory of interest is the minimal candidate for a composite Higgs model that also accommodates a mechanism for top partial compositeness: the Sp(4) gauge theory coupled to two (Dirac) fermions transforming as the fundamental and three as the two-index antisymmetric representation of the gauge group, respectively. We apply an admixture of APE smearing and Wuppertal smearings, as well as the generalized eigenvalue problem approach, to two-point functions involving flavor-singlet mesons, for ensembles having time extent longer than the space extent. We demonstrate that, in the region of lattice parameter space accessible to this study, both masses and mixing angles can be measured effectively, despite the presence of (numerically noisy) contributions from disconnected diagrams.

关键词： Composite models Extensions of Higgs sector Strong interaction Lattice field theory Lattice gauge theory