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Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 876-902页

作者： Xuejuan Chen Zhiping Mao George Em Karniadakis School of Science Jimei UniversityXiamen 361021China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamenChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically,we discretize the resulted Picard integral equation by the SDC method and accelerate the convergence of the SDC iteration by using the generalized minimal residual algorithm(GMRES).We first derive the correction matrix of the SDC method for FDEs and analyze the convergence region of the SDC *** then present several numerical examples for stiff and non-stiff FDEs including fractional linear and nonlinear ODEs as well as fractional phase field models,demonstrating that the accelerated SDC method is much more efficient than the original SDC method,especially for stiff ***,we resolve the issue of low accuracy arising from the singularity of the solutions by using a geometric mesh,leading to highly accurate solutions compared to uniform mesh solutions at almost the same computational ***,for long-time integration of FDEs,using the geometric mesh leads to great computational savings as the total number of degrees of freedom required is relatively small.

关键词： Stiff problem generalized minimal residual geometric mesh refinement long time evolution fractional phase field models

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Variable projection algorithms with sparse constraint for separable nonlinear models

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Control Theory and Technology 2024年第1期22卷 135-146页

作者： Hui-Lang Xu Guang-Yong Chen Si-Qing Cheng Min Gan Jing Chen College of Computer and Data Science Fuzhou UniversityFuzhou350116FujianChina Fujian Key Laboratory of Network Computing and Intelligent Information Processing Fuzhou UniversityFuzhou350116FujianChina Key Laboratory of Intelligent Metro of Universities in Fujian Fuzhou UniversityFuzhou350116FujianChina Engineering Research Center of Big Data Intelligence Ministry of EducationFuzhou UniversityFuzhou350116FujianChina School of Science Jiangnan UniversityWuxi214122JiangsuChina

Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.

关键词： Variable projection(VP) Non-smooth constraint Separable nonlinear models

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Two-Stage Submodular Maximization Under Knapsack Problem

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Tsinghua Science and Technology 2024年第6期29卷 1703-1708页

作者： Zhicheng Liu Jing Jin Donglei Du Xiaoyan Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China College of Taizhou Nanjing Normal UniversityTaizhou 225300China Faculty of Management University of New BrunswickFrederictonE3B 5A3Canada School of Mathematical Science Institute of Mathematicsand Ministry of Education Key Laboratory of NSLSCSNanjing Normal UniversityNanjing 210023China

Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial *** this paper,we consider knapsack *** this problem,we give n articles and m categories,and the goal is to select a subset of articles that can maximize the function F(S).Function F(S)consists of m monotone submodular functions fj,j=1,2,…,m,and each fj measures the similarity of each article in category *** present a constant-approximation algorithm for this problem.

关键词： submodular function knapsack constraint matroid

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High Order Finite Difference Hermite WENO Fixed-Point Fast Sweeping Method for Static Hamilton-Jacobi Equations

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Communications in Computational Physics 2022年第1期31卷 154-187页

作者： Yupeng Ren Yulong Xing Jianxian Qiu School of Mathematical Sciences Xiamen UniversityXiamenFujian 361005P.R.China Department of Mathematics The Ohio State UniversityColumbusOH 43210USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamenFujian 361005P.R.China

In this paper, we combine the nonlinear HWENO reconstruction in [43] andthe fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the staticHamilton-Jacobi equations in a novel HWENO framework recently developed in [22].The proposed HWENO frameworks enjoys several advantages. First, compared withthe traditional HWENO framework, the proposed methods do not need to introduceadditional auxiliary equations to update the derivatives of the unknown function φ.They are now computed from the current value of φ and the previous spatial derivatives of φ. This approach saves the computational storage and CPU time, which greatlyimproves the computational efficiency of the traditional HWENO scheme. In addition,compared with the traditional WENO method, reconstruction stencil of the HWENOmethods becomes more compact, their boundary treatment is simpler, and the numerical errors are smaller on the same mesh. Second, the fixed-point fast sweeping methodis used to update the numerical approximation. It is an explicit method and doesnot involve the inverse operation of nonlinear Hamiltonian, therefore any HamiltonJacobi equations with complex Hamiltonian can be solved easily. It also resolves someknown issues, including that the iterative number is very sensitive to the parameterε used in the nonlinear weights, as observed in previous studies. Finally, to furtherreduce the computational cost, a hybrid strategy is also presented. Extensive numerical experiments are performed on two-dimensional problems, which demonstrate thegood performance of the proposed fixed-point fast sweeping HWENO methods.

关键词： Hermite method Weighted Essentially Non-Oscillatory(WENO)method fixedpoint iteration Hamilton-Jacobi equation hybrid strategy

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A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

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Communications in Computational Physics 2022年第1期31卷 94-130页

作者： Min Zhang Weizhang Huang Jianxian Qiu School of Mathematical Sciences Peking UniversityBeijing100871China Department of Mathematics University of KansasLawrenceKansas 66045USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamenFujian 361005P.R.China

A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake ortsunami waves in the deep ocean. The method combines a quasi-Lagrange movingmesh DG method, a hydrostatic reconstruction technique, and a change of unknownvariables. The strategies in the use of slope limiting, positivity-preservation limiting,and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treatsmesh movement continuously in time and has the advantages that it does not need tointerpolate flow variables from the old mesh to the new one and places no constraintfor the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the wellbalance property, positivity preservation, and high-order accuracy of the method andits ability to adapt the mesh according to features in the flow and bottom topography.

关键词： Well-balance positivity-preserving high-order accuracy quasi-Lagrange moving mesh DG method shallow water equations

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Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws

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Communications in Computational Physics 2022年第7期32卷 364-400页

作者： Jiayin Li Chi-Wang Shu Jianxian Qiu School of Mathematical Sciences Xiamen UniversityXiamenFujian 361005P.R.China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathe-matical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamenFujian 361005P.R.China

In this paper,a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory(HWENO)scheme is designed for hyperbolic conservation *** main idea of this scheme is derived from our previous work[***.,446(2021)110653],in which the integral averages of the function and its first order derivative are used to reconstruct both the function and its first order derivative values at the ***,in this paper,only the function values at the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed by using the information of the zeroth and first order *** addition,an extra modification procedure is used to modify those first order moments in the troubledcells,which leads to an improvement of stability and an enhancement of resolution near *** obtain the same order of accuracy,the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the general HWENO scheme and is more compact than the generalWENO ***,the linear weights are not unique and are independent of the node position,and the CFL number can still be 0.6whether for the one or two dimensional case,which has to be 0.2 in the two dimensional case for other HWENO *** numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.

关键词： Moment-based scheme multi-resolution scheme HWENO scheme hyperbolic conservation laws KXRCF troubled-cell indicator HLLC-flux

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Research on Static Reverse Analysis Technology for Security Detection of Power Industrial Control Software 3

Research on Static Reverse Analysis Technology for Security ...

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3rd International Conference on Intelligent Power and Systems, ICIPS 2023

作者： Chen, Jinshan Yu, Sihang Xie, Xuanxuan Cheng, Yu Tang, Zhijun Deng, Chaoping Li, June State Grid Fujian Electric Power Research Institute Fujian Fuzhou350000 China Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education School of Cyber Science and Engineering Wuhan University Hubei Wuhan430072 China

ISBN: (纸本)9798350328691

In the power industrial control software, defects of software and possible pre-implanted backdoors and malicious codes are important factors that threaten the security of the power industrial control system. The complete and accurate extraction of function call relationship is the basis of software security detection based on function call graph. Therefore, based on analyzing function call sequence of abnormal behavior of electric power industrial control software, a method of software static reverse analysis is proposed. The method identified the function call relationship optimized by the compiler to be a jmp instruction by searching the call/jmp instructions. In order to extract a simplified key function call relationship, a key function list was obtained by performing keyword fuzzy matching. Experiments show that this method can accurately and comprehensively obtain the function call relation, the simplified key function call relationship can improve the efficiency of reverse analysis and provide a better support for software defects, backdoors and malicious codes detection. ©2023 IEEE.

关键词： Industrial research

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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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IF-Font: Ideographic Description Sequence-Following Font Generation 38

IF-Font: Ideographic Description Sequence-Following Font Gen...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Chen, Xinping Ke, Xiao Guo, Wenzhong Fujian Provincial Key Laboratory of Networking Computing and Intelligent Information Processing College of Computer and Data Science Fuzhou University Fuzhou350116 China Engineering Research Center of Big Data Intelligence Ministry of Education Fuzhou350116 China

Few-shot font generation (FFG) aims to learn the target style from a limited number of reference glyphs and generate the remaining glyphs in the target font. Previous works focus on disentangling the content and style features of glyphs, combining the content features of the source glyph with the style features of the reference glyph to generate new glyphs. However, the disentanglement is challenging due to the complexity of glyphs, often resulting in glyphs that are influenced by the style of the source glyph and prone to artifacts. We propose IF-Font, a novel paradigm which incorporates Ideographic Description Sequence (IDS) instead of the source glyph to control the semantics of generated glyphs. To achieve this, we quantize the reference glyphs into tokens, and model the token distribution of target glyphs using corresponding IDS and reference tokens. The proposed method excels in synthesizing glyphs with neat and correct strokes, and enables the creation of new glyphs based on provided IDS. Extensive experiments demonstrate that our method greatly outperforms state-of-the-art methods in both one-shot and few-shot settings, particularly when the target styles differ significantly from the training font styles. The code is available at https://***/Stareven233/IF-Font. © 2024 Neural information processing systems foundation. All rights reserved.

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Cross-Modality Perturbation Synergy Attack for Person Re-identification 38

Cross-Modality Perturbation Synergy Attack for Person Re-ide...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Gong, Yunpeng Zhong, Zhun Qu, Yansong Luo, Zhiming Ji, Rongrong Jiang, Min School of Informatics Xiamen University China School of Computer Science and Information Engineering Hefei University of Technology China The Department of Artificial Intelligence Key Laboratory of Multimedia Trusted Perception and Efficient Computing Ministry of Education of China School of Informatics Key Laboratory of Digital Protection and Intelligent Processing of Intangible CulturalHeritage of Fujian and Taiwan Ministry of Culture and Tourism Xiamen University Fujian Xiamen361005 China

In recent years, there has been significant research focusing on addressing security concerns in single-modal person re-identification (ReID) systems that are based on RGB images. However, the safety of cross-modality scenarios, which are more commonly encountered in practical applications involving images captured by infrared cameras, has not received adequate attention. The main challenge in cross-modality ReID lies in effectively dealing with visual differences between different modalities. For instance, infrared images are typically grayscale, unlike visible images that contain color information. Existing attack methods have primarily focused on the characteristics of the visible image modality, overlooking the features of other modalities and the variations in data distribution among different modalities. This oversight can potentially undermine the effectiveness of these methods in image retrieval across diverse modalities. This study represents the first exploration into the security of cross-modality ReID models and proposes a universal perturbation attack specifically designed for cross-modality ReID. This attack optimizes perturbations by leveraging gradients from diverse modality data, thereby disrupting the discriminator and reinforcing the differences between modalities. We conducted experiments on three widely used cross-modality datasets, namely RegDB, SYSU, and LLCM. The results not only demonstrate the effectiveness of our method but also provide insights for future improvements in the robustness of cross-modality ReID systems. © 2024 Neural information processing systems foundation. All rights reserved.

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