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arXiv 2024年

作者： Li, Yang Liu, Ya-Feng The Shenzhen Research Institute of Big Data Shenzhen518172 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

This paper studies the quality-of-service (QoS) constrained multi-group multicast beamforming design problem, where each multicast group is composed of a number of users requiring the same content. Due to the nonconvex QoS constraints, this problem is nonconvex and NP-hard. While existing optimization-based iterative algorithms can obtain a suboptimal solution, their iterative nature results in large computational complexity and delay. To facilitate real-time implementations, this paper proposes a deep learning-based approach, which consists of a beamforming structure assisted problem transformation and a customized neural network architecture named hierarchical permutation equivariance (HPE) transformer. The proposed HPE transformer is proved to be permutation equivariant with respect to the users within each multicast group, and also permutation equivariant with respect to different multicast groups. Simulation results demonstrate that the proposed HPE transformer outperforms state-of-the-art optimization-based and deep learning-based approaches for multi-group multicast beamforming design in terms of the total transmit power, the constraint violation, and the computational time. In addition, the proposed HPE transformer achieves pretty good generalization performance on different numbers of users, different numbers of multicast groups, and different signal-to-interference-plus-noise ratio targets. Copyright © 2024, The Authors. All rights reserved.

关键词： Beamforming

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Detecting and Exploiting Unit Commitment Structures in MIPs 6

Detecting and Exploiting Unit Commitment Structures in MIPs

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6th International Conference on Power and Energy Technology, ICPET 2024

作者： Su, Zhao-Gang Chen, Sheng-Jie Li, Yu-Fei Chen, Liang Kou, Caixia Cai, Zhi Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Beijing Key Laboratory of Research and System Evaluation of Power Dispatching Automation Technology China Electric Power Research Institute Beijing China

ISBN: (纸本)9798350375855

The unit commitment (UC) problem has been extensively researched in the literature, which is typically formulated as a mixed integer programming (MIP) problem. However, current studies lack effective methods to identify potential UC problem structures within a general MIP problem, making it challenging to leverage well-established valid inequalities for UC problems to accelerate the solution process. In this paper, we present a novel detection method that automatically identifies UC structures within an MIP problem by analyzing the relationships between variables and constraints. Moreover, we enhance the MIP formulation by incorporating three well-studied classes of valid inequalities as cutting planes, based on the identified UC structures. Our experiments demonstrate that our proposed UC detection method greatly improves computational efficacy of a standard MIP solver compared to the default setting. © 2024 IEEE.

关键词： Mixed-integer linear programming

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Shape of my heart: Cardiac models through learned signed distance functions 7

Shape of my heart: Cardiac models through learned signed dis...

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7th International Conference on Medical Imaging with Deep Learning, MIDL 2024

作者： Verhülsdonk, Jan Grandits, Thomas Costabal, Francisco Sahli Pinetz, Thomas Krause, Rolf Auricchio, Angelo Haase, Gundolf Pezzuto, Simone Effland, Alexander Institute for Applied Mathematics University of Bonn Germany Department of Mathematics and Scientific Computing University of Graz Austria Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Chile Center for Computational Medicine in Cardiology Università della Svizzera Italiana Switzerland FernUni Schweiz Brig Switzerland Instituto Cardiocentro Ticino EOC Switzerland Department of Mathematics University of Trento Italy

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM). © 2024 CC-BY 4.0, J. Verhülsdonk et al.

关键词： Image segmentation

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Phase-field-based lattice Boltzmann method for containerless freezing

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Physical Review E 2024年第3期110卷 035301页

作者： Jiangxu Huang Lei Wang Zhenhua Chai Baochang Shi School of Mathematics and Statistics School of Mathematics and Physics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing

In this paper we first propose a phase-field model for the containerless freezing problems, in which the volume expansion or shrinkage of the liquid caused by the density change during the phase change process is considered by adding a mass source term to the continuum equation. Then a phase-field-based lattice Boltzmann (LB) method is further developed to simulate solid-liquid phase change phenomena in multiphase systems. We test the developed LB method by the problem of conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, and the droplet solidification on a cold surface, and the numerical results are in agreement with the analytical and experimental solutions. In addition, the LB method is also used to study the rising bubbles with solidification. The results of the present method not only accurately capture the effect of bubbles on the solidification process, but also are in agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle.

关键词： Drops & bubbles Liquid-solid phase transition

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Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator

arXiv

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arXiv 2024年

作者： Xu, Shu Cao, Liqun School of Mathematical Sciences Peking University Beijing100871 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We present a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model, which is the most popular model for lithium-ion batteries. Central to our approach is a novel projection operator designed for the pseudo-(N+1)-dimensional equation, offering a powerful tool for multiscale equation analysis. Our results bridge a gap in the analysis for dimensions 2 ≤N ≤3 and achieve optimal convergence rates of h+(∆r)2. Additionally, we perform a detailed numerical verification, marking the first such validation in this context. By avoiding the change of variables, our error analysis can also be extended beyond isothermal conditions. Copyright © 2024, The Authors. All rights reserved.

关键词： Discrete element methods

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Mixed finite element methods for biharmonic obstacle problems

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SeMA Journal 2025年 1-10页

作者： Piersanti, Paolo Sun, Tianyu School of Science and Engineering The Chinese University of Hong Kong (Shenzhen) 2001 Longxiang Blvd. Longgang District Shenzhen China Department of Mathematics and Institute for Scientific Computing and Applied Mathematics Indiana University Bloomington 729 East Third Street Bloomington IN United States

This paper is devoted to the study of an alternative Finite Element Method to the one originally proposed by Ciarlet & Raviart, and then complemented by Ciarlet & Glowinski, for studying the numerical approximation of the solution of the biharmonic problem. In addition to providing an alternative way of approximating the solution of the biharmonic problem, the method here presented is valid also in the context where the solution to the biharmonic problem is subjected to a constraint. The theoretical results we derived are complemented by a series of numerical experiments. © The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada 2025.

关键词： Elasticity theory Finite element method Obstacle problems Penalty method Variational inequalities

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Precise Analysis of Covariance Identifiability for Activity Detection in Grant-Free Random Access

arXiv

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arXiv 2024年

作者： Luo, Shengsong Ma, Junjie Xu, Chongbin Wang, Xin the Department of Communication Science and Engineering Fudan University Shanghai200433 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

We consider the identifiability issue of maximum-likelihood based activity detection in massive MIMO-based grant-free random access. An intriguing observation by Chen et al. [1] indicates that the identifiability undergoes a phase transition for commonly-used random user signatures as L2, N and K tend to infinity with fixed ratios, where L, N and K denote the user signature length, the total number of users, and the number of active users, respectively. In this letter, we provide a precise analytical characterization of the phase transition based on a spectral universality conjecture. Numerical results demonstrate excellent agreement between our theoretical predictions and the empirical phase transitions. Copyright © 2024, The Authors. All rights reserved.

关键词： Maximum likelihood

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Streaming Algorithms for Non-Submodular Maximizationon the Integer Lattice

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Tsinghua Science and Technology 2023年第5期28卷 888-895页

作者： Jingjing Tan Yue Sun Yicheng Xu Juan Zou School of Mathematics and Information Science Weifang UniversityWeifang 261061China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Shenzhen Institute of Advanced Technology Chinese Academy of SciencesShenzhen 518055China School of Mathematical Sciences Qufu Normal UniversityQufu 273165China

Many practical problems emphasize the importance of not only knowing whether an element is selectedbut also deciding to what extent it is selected,which imposes a challenge on submodule *** this study,we consider the monotone,nondecreasing,and non-submodular maximization on the integer lattice with a *** first design a two-pass streaming algorithm by refining the estimation interval of the optimal *** element,the algorithm not only decides whether to save the element but also gives the number of ***,we introduce the binary search as a subroutine to reduce the time ***,we obtain a one-passstreaming algorithm by dynamically updating the estimation interval of optimal ***,we improve the memorycomplexity of this algorithm.

关键词： integer lattice non-submodular streaming algorithm cardinality constraint

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AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS

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Journal of computational mathematics 2021年第6期39卷 848-864页

作者： Liang Yan Tao Zhou School of Mathematics Southeast UniversityNanjing210096China Nanjing Center for Applied Mathematics Nanjing211135China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive forcomplexity problems due to repetitive evaluations of the expensive forward model and itsgradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO. In particular,we propose to drawn the training points for the DNN-surrogate from a local approximatedposterior distribution – yielding a flexible and efficient sampling algorithm that convergesto the direct RTO approach. We present a Bayesian inverse problem governed by ellipticPDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach, which shows that DNN-RTO can significantly outperform the traditional RTO.

关键词： Bayesian inverse problems Deep neural network Markov chain Monte Carlo

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An Optimization Method for Renewable Energy and Energy Storage Capacity Allocation Based on Temporal Production Simulation 7

An Optimization Method for Renewable Energy and Energy Stora...

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7th IEEE Conference on Energy Internet and Energy System Integration, EI2 2023

作者： Du, Hongbo Li, Chi Chen, Liang Zhang, Jinping Kou, Caixia College of Sciences Beijing University of Posts and Telecommunications Beijing China National Key Laboratory of Renewable Energy Grid-Integration China Electric Power Research Institute Beijing China Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

ISBN: (纸本)9798350345094

With the rapid expansion of large-scale renewable energy bases in China, optimizing the allocation of renewable energy and energy storage capacity is crucial for improving system efficiency. In this paper, a joint optimal configuration method of wind-photovoltaic-energy storage capacity based on time series production simulation is proposed for renewable energy transmission base. Its aim is to minimize the total investment cost of the system under certain constraints about the proportion of renewable energy power generation, renewable energy utilization rate, conventional thermal power operation, energy storage power station operation, ultra-high voltage direct current (UHVDC) regulation and power transmission. To handle the nonlinear constraints, linearization is achieved by introducing integer variables. For the complex operation constraints of conventional thermal power and UHVDC channel, a simplified modeling method of start-stop cycle and adjustment cycle is proposed, which can effectively reduce the number of integer variables and improve the solving efficiency. The effectiveness of the proposed method is tested on the data of a renewable energy base in Northwest China. © 2023 IEEE.

关键词： Energy utilization

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