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arXiv 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

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RECOVERY TYPE A POSTERIORI ERROR ESTIMATION OF AN ADAPTIVE FINITE ELEMENT METHOD FOR CAHN-HILLIARD EQUATION

arXiv

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arXiv 2023年

作者： Chen, Yaoyao Huang, Yunqing Yi, Nianyu Yin, Peimeng School of Mathematics and Statistics Anhui Normal University Wuhu241000 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Multiscale Methods and Dynamics Group Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn-Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time reconstruction technique based on three time-level approximations, resulting in an optimal a posteriori error estimator. We propose a time-space adaptive algorithm that utilizes the derived a posteriori error estimator as error indicators. Numerical experiments are presented to validate the theoretical findings, including comparing with an adaptive finite element method based on a residual type a posteriori error estimator. © 2023, CC BY-NC-ND.

关键词： Recovery

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Multifractal analyses of daily rainfall time series in Pearl River basin of China

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Physica A: Statistical Mechanics and its Applications 2014年 405卷 193-202页

作者： Zu-Guo Yu Yee Leung Yongqin David Chen Qiang Zhang Vo Anh Yu Zhou Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia Department of Geography and Resource Management The Chinese University of Hong Kong Hong Kong China Institute of Environment Energy and Sustainability The Chinese University of Hong Kong Hong Kong China Department of Water Resources and Environment Sun Yat-sen University Guangzhou 510275 China Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education Institute Sun Yat-sen University Guangzhou 510275 China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K ( q ) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter H from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h ( 2 ) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K ( 2 ) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

关键词： Daily rainfall time series Multifractal property Universal multifractal model Multifractal detrended fluctuation analysis

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A Novel Preference-Driven Dynamic Multi-Objective Evolutionary Algorithm for Solving Dynamic Multi-Objective Problems

SSRN

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SSRN 2024年

作者： Wang, Xueqing Zheng, Jinhua Hou, Zhanglu Liu, Yuan Zou, Juan Xia, Yizhang Yang, Shengxiang Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Computer Science School of Cyberspace Science of Xiangtan University Hunan Province Xiangtan China Faculty of School of Computer Science School of Cyberspace Science of Xiangtan University Xiangtan411105 China School of Computer Science and Informatics De Montfort University LeicesterLE1 9BH United Kingdom

Most studies in dynamic multi-objective optimization have predominantly focused on rapidly and accurately tracking changes in the Pareto optimal front (POF) and Pareto optimal set (POS) when the environment undergoes changes. However, there are real-world scenarios where it is necessary to simultaneously solve changing objective functions and satisfy the preference of Decision Makers (DMs). In particular, the DMs may be only interested in a partial region of the POF, known as the region of interest (ROI), rather than requiring the entire POF. To meet the challenge of simultaneously predicting a changing POF and/or POS and dynamic ROI, this paper proposes a new dynamic multi-objective evolutionary algorithm (DMOEAs) based on the preference. The proposed algorithm consists of three key components: an evolutionary direction adjustment strategy based on changing reference points to accommodate shifts in preferences, an angle-based search strategy for tracking the varying ROI, and a hybrid prediction strategy that combines linear prediction models and population manifold estimation within the ROI to ensure convergence and distribution in scenarios where preferences remain unchanged. Experimental studies conducted on 16 widely used benchmark problems and empirical results demonstrate the significant advantages of the proposed algorithm over existing state-of-the-art DMOEAs. © 2024, The Authors. All rights reserved.

关键词： Evolutionary algorithms

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Dynamic Constrained Multi-Objective Optimization Algorithm Based on Co-Evolution and Diversity Enhancement

SSRN

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SSRN 2023年

作者： Che, Wang Zheng, Jinhua Hu, Yaru Zou, Juan Yang, Shengxiang Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Computer Science School of Cyberspace Science of Xiangtan University Hunan Province Xiangtan China Faculty of School of Computer Science School of Cyberspace Science of Xiangtan University Xiangtan411105 China School of Computer Science and Informatics De Montfort University LeicesterLE1 9BH United Kingdom

Dynamic constrained multi-objective optimization problems (DCMOPs) involve objectives, constraints, and parameters that change over time. This kind of problem presents a greater challenge for evolutionary algorithms because it requires the population to quickly track the changing pareto-optimal set (PS) while being subject to constrained limitations and maintaining a good distribution of solutions. This paper proposes a dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement (CEDE). The static optimization part involves the co-evolution of three populations. We evolve the first population to prioritize the preservation of feasible individuals. The second population is evolved to assist the first population in finding better feasible regions, while the third population is evolved to aid the first population in exploring feasible regions comprehensively. At different stages, the co-evolution of these three populations will also be adjusted. Additionally, to prevent the elimination of potentially valuable infeasible individuals due to pareto domination, we employ an archive set to store and update these individuals. When the environment changes, we propose a diversity enhancement strategy, which includes a diversity maintenance strategy and a center point-based exploration strategy. The experimental results demonstrate that CEDE is highly competitive in handling DCMOPs compared to several state-of-the-art algorithms. © 2023, The Authors. All rights reserved.

关键词： Evolutionary algorithms

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Weak Relationship Indicator-Based Evolutionary Algorithm for Multimodal Multi-Objective Optimization

SSRN

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SSRN 2023年

作者： Xiang, Yi Zheng, Jinhua Hu, Yaru Liu, Yuan Zou, Juan Deng, Qi Yang, Shengxiang Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Computer Science School of Cyberspace Science of Xiangtan University Hunan Province Xiangtan China Faculty of School of Computer Science School of Cyberspace Science of Xiangtan University Xiangtan411105 China School of Computer Science and Informatics De Montfort University LeicesterLE1 9BH United Kingdom

Multimodal multi-objective problems (MMOPs) refer to multiple equivalent Pareto sets (PSs) that can be mapped to the same Pareto optimal front (PF) and have widespread applications in real life. Traditional multimodal multiobjective algorithms (MMEAs) use strong relationships (such as global domination relationships and global indicators) to guide population convergence. This may lead to two problems: first, when there are PSs with different search difficulties, the population will tend to explore the easier-to-search PSs and lose the more difficult-to-search PSs. Second, it cannot retain local PSs well (slightly worse in the objective space but far apart in the decision space). To address these issues, we propose a weak relationship indicator-based MMEA that includes weak convergence indicators and density evaluation indicators. The weak convergence indicator considers the relationship between an individual and a certain number of its neighbors. The density evaluation indicator comprehensively considers the density information of the individual and its neighbors. This allows the population to retain solutions from different PSs during exploration, even local PSs. In addition, an archive based on weak convergence indicators also retains excellent solutions generated during the evolution of the population. Experimental results show that our algo-rithm has higher competitive performance than seven other state-of-the-art MMEAs on chosen benchmark problems. © 2023, The Authors. All rights reserved.

关键词： Multiobjective optimization

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Dynamic Constrained Multi-Objective Optimization Algorithm Based on Co-Evolution and Diversity Enhancement

SSRN

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SSRN 2024年

Dynamic constrained multi-objective optimization problems (DCMOPs) involve objectives, constraints, and parameters that change over time. This kind of problem presents a greater challenge for evolutionary algorithms because it requires the population to quickly track the changing pareto-optimal set (PS) while being subject to constrained limitations and maintaining a good distribution of solutions. This paper proposes a dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement (CEDE). The static optimization involves the co-evolution of three populations. We evolve the first population to prioritize the preservation of feasible individuals. The second population is evolved to assist the first population in finding better feasible regions, while the third population is evolved to aid the first population in exploring feasible regions comprehensively. At different stages, the co-evolution of these three populations will also be adjusted. Additionally, to prevent the elimination of potentially valuable infeasible individuals due to pareto domination, we employ an archive set to store and update these individuals, providing more useful information for both static and dynamic optimization. When the environment changes, we propose a diversity enhancement strategy, which includes a diversity maintenance strategy and a center point-based exploration strategy. The experimental results demonstrate that CEDE is highly competitive in handling DCMOPs compared to several state-of-the-art algorithms. © 2024, The Authors. All rights reserved.

关键词： Evolutionary algorithms

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IF2Net: Innately Forgetting-Free Networks for Continual Learning

arXiv

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arXiv 2023年

作者： Li, Depeng Wang, Tianqi Xu, Bingrong Kawaguchi, Kenji Zeng, Zhigang Suganthan, Ponnuthurai Nagaratnam The School of Artificial Intelligence and Automation The Institute of Artificial Intelligence Huazhong University of Science and Technology The Key Laboratory of Image Processing and Intelligent Control Education Ministry of China Wuhan430074 China The School of Automation Wuhan University of Technology Wuhan430070 China The School of Computing National University of Singapore 117417 Singapore The School of Electrical and Electronic Engineering Nanyang Technological University Singapore639798 Singapore The KINDI Center for Computing Research College of Engineering Qatar University Doha Qatar

Continual learning can incrementally absorb new concepts without interfering with previously learned knowledge. Motivated by the characteristics of neural networks, in which information is stored in weights on connections, we investigated how to design an Innately Forgetting-Free Network (IF2Net) for continual learning context. This study proposed a straightforward yet effective learning paradigm by ingeniously keeping the weights relative to each seen task untouched before and after learning a new task. We first presented the novel representation-level learning on task sequences with random weights. This technique refers to tweaking the drifted representations caused by randomization back to their separate task-optimal working states, but the involved weights are frozen and reused (opposite to well-known layer-wise updates of weights). Then, sequential decision-making without forgetting can be achieved by projecting the output weight updates into the parsimonious orthogonal space, making the adaptations not disturb old knowledge while maintaining model plasticity. IF2Net allows a single network to inherently learn unlimited mapping rules without telling task identities at test time by integrating the respective strengths of randomization and orthogonalization. We validated the effectiveness of our approach in the extensive theoretical analysis and empirical study. Copyright © 2023, The Authors. All rights reserved.

关键词： Decision making

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Risk analysis of physical protection system based on evidence theory

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Journal of Information and Computational Science 2010年第13期7卷 2871-2878页

作者： Xu, Peida Su, Xiaoyan Wu, Jiyi Sun, Xiaohong Zhang, Yajuan Deng, Yong College of Computer and Information Sciences Southwest University Chongqing 400715 China Hangzhou Key Lab of E-Business and Information Security Hangzhou Normal University Zhejiang 310036 China College of Food Science and Technology Shanghai Ocean University Shanghai 201306 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 China Key Subject Laboratory of National defense for Radioactive Waste and Environmental Security Southwest University of Science and Technology Mianyang 621010 China School of Electronics and Information Technology Shanghai Jiao Tong University Shanghai 200240 China

Risk evaluation is very important to the design and improvement of physical protection systems. In this paper, an evaluation method of multi-source information fusion is proposed based on the D-S evidence theory. In the proposed method, each individual component of the protection system in the simulated plane is modeled. Then, the threat report of each component according to the specific tactics is determined based on its real environment. Finally, the comprehensive threat distribution is obtained based on through the D-S evidence theory to combine multi-sources information. The proposed method can easily applied to the evaluation of the effectiveness of the protection system. We make the total threat of the protection system lowest through changes of the protection resources allocation. A numerical example is used to illustrate the efficiency of the proposed method. Copyright © 2010 Binary Information Press.

关键词： Information fusion

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Detection of Deepfake videos using long distance attention

arXiv

引用

arXiv 2021年

作者： Lu, Wei Liu, Lingyi Luo, Junwei Zhao, Xianfeng Zhou, Yicong Huang, Jiwu School of Computer Science and Engineering Guangdong Province Key Laboratory of Information Security Technology Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen University Guangzhou510006 China State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences Beijing100195 China School of Cyber Security University of Chinese Academy of Sciences Beijing100195 China Department of Computer and Information Science University of Macau 999078 China Guangdong Key Laboratory of Intelligent Information Processing Shenzhen Key Laboratory of Media Security Shenzhen University Shenzhen518060 China Shenzhen Institute of Artificial Intelligence and Robotics for Society Shenzhen518055 China

With the rapid progress of deepfake techniques in recent years, facial video forgery can generate highly deceptive video contents and bring severe security threats. And detection of such forgery videos is much more urgent and challenging. Most existing detection methods treat the problem as a vanilla binary classification problem. In this paper, the problem is treated as a special fine-grained classification problem since the differences between fake and real faces are very subtle. It is observed that most existing face forgery methods left some common artifacts in the spatial domain and time domain, including generative defects in the spatial domain and inter-frame inconsistencies in the time domain. And a spatial-temporal model is proposed which has two components for capturing spatial and temporal forgery traces in global perspective respectively. The two components are designed using a novel long distance attention mechanism. The one component of the spatial domain is used to capture artifacts in a single frame, and the other component of the time domain is used to capture artifacts in consecutive frames. They generate attention maps in the form of patches. The attention method has a broader vision which contributes to better assembling global information and extracting local statistic information. Finally, the attention maps are used to guide the network to focus on pivotal parts of the face, just like other fine-grained classification methods. The experimental results on different public datasets demonstrate that the proposed method achieves the state-of-the-art performance, and the proposed long distance attention method can effectively capture pivotal parts for face forgery. Copyright © 2021, The Authors. All rights reserved.

关键词： Time domain analysis

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