检索结果-内蒙古大学图书馆

ERROR ANALYSIS OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS

Journal of computational Mathematics 2025年第3期43卷 731-770页

作者： Ying Yang Ya Liu Yang Liu Shi Shu School of Mathematics and Computational Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationCenter for Applied Mathematics of Guangxi(GUET)Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computational Science Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105China

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion *** presenting the semi-discrete scheme,the optimal H1 norm error estimates are presented for the time-dependent PNP equations,which are based on some error estimates of a virtual element energy *** Gummel iteration is used to decouple and linearize the PNP equations and the error analysis is also given for the iteration of fully discrete virtual element *** numerical experiment on different polygonal meshes verifies the theoretical convergence results and shows the efficiency of the virtual element method.

关键词： Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration

来源：评论

学校读者我要写书评

暂无评论

FREQUENCY-BASED REDUCED MODELS FROM PURELY TIME-DOMAIN data VIA data INFORMATIVITY

引用

SIAM Journal on Scientific Computing 2025年第2期47卷 A1225-A1250页

作者： Ackermann, Michael S. Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Frequency-based methods have been successfully employed in creating high-fidelity data-driven reduced order models (DDROMs) for linear dynamical systems. These methods require access to values (and sometimes derivatives) of the frequency-response function (transfer function) in the complex plane. These frequency domain values can at times be costly or difficult to obtain (especially if the method of choice requires resampling);instead one may have access to only time-domain input-output data. The data informativity approach to moment matching provides a powerful new framework for recovering the required frequency data from a single time-domain trajectory. In this work, we analyze and extend upon this framework, resulting in significantly improved conditioning of the associated linear systems, an error indicator, and the removal of an assumption that the system order is known. This analysis leads to a robust algorithm for recovering frequency information from time-domain data, suitable for large-scale systems. We demonstrate the effectiveness of our algorithm by forming frequency-based DDROMs from time-domain data of several dynamical systems. © 2025 Society for Industrial and Applied Mathematics.

关键词： data assimilation

来源：评论

学校读者我要写书评

暂无评论

A data representation method using distance correlation

引用

Frontiers of Computer science 2025年第1期19卷 1-14页

作者： Xinyan LIANG Yuhua QIAN Qian GUO Keyin ZHENG Institute of Big Data Science and Industry Shanxi UniversityTaiyuan 030006China Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education Shanxi UniversityTaiyuan 030006China School of Computer Science and Technology Taiyuan University of Science and TechnologyTaiyuan 030024China Shanxi Key Laboratory of Big Data Analysis and Parallel Computing Taiyuan University of Science and TechnologyTaiyuan 030024China

Association in-between features has been demonstrated to improve the representation ability of data. However, the original association data reconstruction method may face two issues: the dimension of reconstructed data is undoubtedly higher than that of original data, and adopted association measure method does not well balance effectiveness and efficiency. To address above two issues, this paper proposes a novel association-based representation improvement method, named as AssoRep. AssoRep first obtains the association between features via distance correlation method that has some advantages than Pearson’s correlation coefficient. Then an improved matrix is formed via stacking the association value of any two features. Next, an improved feature representation is obtained by aggregating the original feature with the enhancement matrix. Finally, the improved feature representation is mapped to a low-dimensional space via principal component analysis. The effectiveness of AssoRep is validated on 120 datasets and the fruits further prefect our previous work on the association data reconstruction.

关键词： association representation distance correlation classification

来源：评论

学校读者我要写书评

暂无评论

IRKA Is a Riemannian Gradient Descent Method

引用

IEEE Transactions on Automatic Control 2025年第5期70卷 2979-2991页

作者： Mlinaric, Petar Beattie, Christopher A. Drmac, Zlatko Gugercin, Serkan Virginia Tech Department of Mathematics BlacksburgVA24061 United States University of Zagreb Faculty of Natural Sciences Zagreb10000 Croatia Virginia Tech Department of Mathematics and Division of Computational Modeling and Data Analytics Academy of Data Science BlacksburgVA24061 United States

The iterative rational Krylov algorithm (IRKA) is a commonly used fixed point iteration developed to minimize the H2 model order reduction error. In this work, the IRKA is recast as a Riemannian gradient descent method with a fixed step size over the manifold of rational functions having fixed degree. This interpretation motivates the development of a Riemannian gradient descent method utilizing as a natural extension variable step size and line search. Comparisons made between the IRKA and this extension on a few examples demonstrate significant benefits. © 1963-2012 IEEE.

关键词： Rational functions

来源：评论

学校读者我要写书评

暂无评论

Granular Sequential Three-Way Decision for Specific Decision Classes

引用

IEEE Transactions on Fuzzy Systems 2025年第5期33卷 1650-1663页

作者： Cheng, Yunlong Yang, Xiuhua Zhang, Qinghua Shao, Yabin Wang, Guoyin Chongqing University of Posts and Telecommunications School of Science Chongqing400065 China Chongqing University of Posts and Telecommunications Chongqing Key Laboratory of Tourism Multisource Data Perception and Decision Ministry of Culture and Tourism Key Laboratory of Big Data Intelligence Computing Chongqing Key Laboratory of Computational Intelligence Chongqing400065 China

Sequential three-way decision (S3WD) is an efficient granular computing paradigm for dealing with uncertain problems. However, it is primarily oriented to all decision classes, which contradicts the fact that decisions are typically for the specific decision classes. Meanwhile, most S3WD models hide the topological structure of the granules, leading to difficulties in semantic interpretation. To address the issues, integrating model construction, attribute reduction and knowledge extraction, a general framework of granular sequential three-way decision (GrS3WD) for the specific decision classes is proposed to improve semantic interpretation and computational efficiency. First, a two-stage trisecting strategy and a GrS3WD model are proposed to integrate model construction with attribute reduction. Its main advantage is that it retains the topological structure of granules, which not only enhances semantic interpretation but also avoids unnecessary double counting. Second, three acceleration strategies and a novel granular sequential three-way reduction (GrS3WR) algorithm are proposed to fast obtain a classification-based reduct or a class-specific reduct. Finally, the decision rules with multi-granularity can be directly extracted from the concept tree generated by GrS3WR. Experimental results demonstrate that a class-specific reduct usually has fewer attributes and better classification performance than a classification-based reduct. Moreover, GrS3WR can significantly improve the computational efficiency of attribute reduction. © 1993-2012 IEEE.

关键词： Granular computing

来源：评论

学校读者我要写书评

暂无评论

Selecting Central and Divergent Samples via Leading Tree Metric Space for Semisupervised Learning

引用

IEEE Transactions on Fuzzy Systems 2025年第5期33卷 1578-1591页

作者： Xu, Ji Ren, Gang Tang, Jianhang Ding, Weiping Wang, Guoyin Guizhou University State Key Laboratory of Public Big Data Guiyang550025 China Nantong University School of Artificial Intelligence and Computer Science Nantong226019 China City University of Macau Faculty of Data Science 999078 China Chongqing Normal University Chongqing400065 China Chongqing University of Posts and Telecommunications Chongqing Key Laboratory of Computational Intelligence Chongqing400065 China

The distribution of the labeled data can greatly affect the performance of a semisupervised learning (SSL) model. Most existing SSL models select the labeled data randomly and equally allocate the labeling quota among the classes, leading to considerable unstableness and degeneration of performance. This study unsupervisedly constructs a leading forest that forms another metric space, based on which it is convenient to define the fuzzy membership function to characterize central and divergent samples and select both types with fuzzy Xor logic. The labeling quota can, thus, be allocated adaptively among different classes. The proposed determinate labeling strategy can generally improve the performance for most SSLs. Especially, when combined with the kernelized large margin component analysis, it produces a novel semisupervised classification model. In addition, the multimodal issue in SSL is effectively addressed by the multigranular structure of leading forest that readily facilitates multiple local metrics learning. Extensive experimental results demonstrate that the proposed method achieved competitive efficiency and encouraging accuracy when compared with the state-of-the-art methods. © 1993-2012 IEEE.

关键词： Self-supervised learning

来源：评论

学校读者我要写书评

暂无评论

Predator Prey Scavenger Model using Holling’s Functional Response of Type III and Physics-Informed Deep Neural Networks

引用

International Journal of Applied and computational Mathematics 2025年第2期11卷 1-32页

作者： Panchal, Aneesh Beniwal, Kirti Kumar, Vivek Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore 560012 India Department of Applied Mathematics Delhi Technological University Delhi New Delhi 110042 India

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka–Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator–prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling’s functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden–Fletcher–Goldfarb–Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.

关键词： Broyden–Fletcher–Goldfarb–Shanno optimization Physics-informed deep neural network Predator prey scavenger model Stability analysis

来源：评论

学校读者我要写书评

暂无评论

Interpolatory model reduction of dynamical systems with root mean squared error 11

Interpolatory model reduction of dynamical systems with root...

引用

11th Vienna International Conference on Mathematical Modelling, MATHMOD 2025

作者： Reiter, Sean Werner, Steffen W.R. Department of Mathematics Virginia Tech BlacksburgVA24061 United States Department of Mathematics and Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

The root mean squared error is an important measure used in a variety of applications like structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity quickly become computationally prohibitive. Model order reduction techniques resolve this issue via the construction of surrogate models that emulate the root mean squared error measure using an intermediate linear system. However, classical approaches require a large number of system outputs, which is disadvantageous in the design of reduced-order models. In this work, we consider directly the root mean squared error as the quantity of interest using the concept of quadratic-output models and propose several new model reduction techniques for the construction of appropriate surrogates. Numerical tests are performed on a model of a plate with tuned vibration absorbers. Copyright © 2025 The Authors.

关键词： Mean square error

来源：评论

学校读者我要写书评

暂无评论

Automated Quality Assessment Using Appearance-Based Simulations and Hippocampus Segmentation on Low-Field Paediatric Brain MR Images 1st

Automated Quality Assessment Using Appearance-Based Simulati...

引用

1st MICCAI Challenge on Low Field Pediatric Brain Magnetic Resonance Image Segmentation and Quality Assurance, LISA 2024, held in Conjunction with Medical Image Computing and Computer Assisted Intervention Conference, MICCAI 2024

作者： Sundaresan, Vaanathi Dinsdale, Nicola K Department of Computational and Data Sciences Indian Institute of Science Bangalore560012 India Oxford Machine Learning in NeuroImaging Lab Department of Computer Science University of Oxford Oxford United Kingdom

ISBN: (纸本)9783031830105

Understanding the structural growth of paediatric brains is a key step in the identification of various neuro-developmental disorders. However, our knowledge is limited by many factors, including the lack of automated image analysis tools, especially in Low and Middle Income Countries from the lack of high field MR images available. Low-field systems are being increasingly explored in these countries, and, therefore, there is a need to develop automated image analysis tools for these images. In this work, as a preliminary step, we consider two tasks: 1) automated quality assurance and 2) hippocampal segmentation, where we compare multiple approaches. For the automated quality assurance task a DenseNet combined with appearance-based transformations for synthesising artefacts produced the best performance, with a weighted accuracy of 82.3%, thus ranking in the 1st place in the LISA2024 Challenge. For the segmentation task, registration of an average atlas performed the best, with a final Dice score of 0.61. Our results show that although the images can provide understanding of large scale pathologies and gross scale anatomical development, there still remain barriers for their use for more granular analyses. © The Author(s) 2025.

关键词： Magnetic resonance imaging

来源：评论

学校读者我要写书评

暂无评论

Secured and Privacy-Preserving GPU-Based Machine Learning Inference in Trusted Execution Environment: A Comprehensive Survey 17

Secured and Privacy-Preserving GPU-Based Machine Learning In...

引用

17th International Conference on COMmunication Systems and NETworkS, COMSNETS 2025

作者： Chaudhuri, Arunava Shukla, Shubhi Bhattacharya, Sarani Mukhopadhyay, Debdeep Indian Institute of Technology Kharagpur Department of Computer Science and Engineering Kharagpur India Indian Institute of Technology Kharagpur Centre for Computational and Data Sciences Kharagpur India

ISBN: (纸本)9798331531195

With the rapid advancement of machine learning (ML) models and their widespread application across various sectors such as intrusion detection, medical diagnosis, natural language processing, and autonomous driving, these technologies have achieved remarkable success. However, this progress has also raised significant concerns about ensuring the security of ML models and protecting both private training data and model outputs from getting exposed in a shared cloud environment. To address these challenges, researchers have proposed various methodologies to create privacy-preserving, secure, and trustworthy model execution environments to prevent adversarial attacks. This study provides a comprehensive review of Trusted Execution Environment (TEE) implementations across different hardware accelerators. It also offers an overview of modern techniques for preserving privacy and security in execution environments, while identifying critical research gaps that require attention. In essence, this survey is an important resource for researchers, providing insights into recent methodologies and guiding them to focus on pressing research challenges. © 2025 IEEE.

关键词： Adversarial machine learning

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：