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Error Analysis of Virtual Element Method for the Poisson-Boltzmann Equation

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arXiv 2023年

作者： Huang, Linghan Shu, Shi Yang, Ying Guangxi Guilin541004 China School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Xiangtan411105 China Guangxi541004 China

The Poisson-Boltzmann equation is a nonlinear elliptic equation with Dirac distribution sources, which has been widely applied to the prediction of electrostatics potential of biological biomolecular systems in solution. In this paper, we discuss and analysis the virtual element method for the Poisson-Boltzmann equation on general polyhedral meshes. Under the low regularity of the solution of the whole domain, nearly optimal error estimates in both L2-norm and H1-norm for the virtual element approximation are obtained. The numerical experiment on different polyhedral meshes shows the efficiency of the virtual element method and verifies the proposed theoretical prediction. Copyright © 2023, The Authors. All rights reserved.

关键词： Poisson equation

Machine learning prediction of network dynamics with privacy protection

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arXiv 2022年

作者： Xia, Xin Su, Yansen Lü, Linyuan Zhang, Xingyi Lai, Ying-Cheng Zhang, Hai-Feng The Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Mathematical Science Anhui University Hefei230601 China The Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Artificial Intelligence Anhui University Hefei230601 China Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of China Chengdu610054 China School of Electrical Computer and Energy Engineering Arizona State University TempeAZ85287 United States

Predicting network dynamics based on data, a problem with broad applications, has been studied extensively in the past, but most existing approaches assume that the complete set of historical data from the whole network is available. This requirement presents a great challenge in applications, especially for large, distributed networks in the real world, where data collection is accomplished by many clients in a parallel fashion. Often, each client only has the time series data from a partial set of nodes and the client has access to only partial timestamps of the whole time series data and partial structure of the network. Due to privacy concerns or license related issues, the data collected by different clients cannot be shared. To accurately predict the network dynamics while protecting the privacy of different parties is a critical problem in the modern time. Here, we propose a solution based on federated graph neural networks (FGNNs) that enables the training of a global dynamic model for all parties without data sharing. We validate the working of our FGNN framework through two types of simulations to predict a variety of network dynamics (four discrete and three continuous dynamics). As a significant real-world application, we demonstrate successful prediction of State-wise influenza spreading in the USA. Our FGNN scheme represents a general framework to predict diverse network dynamics through collaborative fusing of the data from different parties without disclosing their privacy. © 2022, CC BY.

关键词： Forecasting

Self-Organizing Coverage Method of Swarm Robots Based on Dynamic Virtual Force

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SSRN

SSRN 2024年

作者： Wang, Qiuzhen Zheng, Yue Zou, Juan Liu, Yuan Jianquan, Ouyang 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

Swarm robots often cover designated areas to complete specific tasks, such as forest firefighting or ocean oil spill cleaning. The robot has the ability for local perception and limitedcommunication with surrounding robots, then it is difficult to cope with coverage tasks indynamic environments. This paper proposes a self-organization algorithm for swarm robotsbased on Dynamic Virtual Force (DVF) to cover the dynamic area. One robot in the swarmcan locally perceive the surrounding robots and dynamically select some adjacent robots togenerate virtual repulsion to control its own movement. The swarm robot can be deployed quicklyand uniformly in unknown areas, while being able to adapt itself to changes in dynamic ***, it can adaptively cover parts of an area with different densities, which are dividedaccording to the needs of the area, and different densities require different numbers of robots tobe assigned. We design several groups of simulation experiments, and the results show that thealgorithm achieves good coverage performance and verifies the effectiveness and superiority ofthe method based on DVF. © 2024, The Authors. All rights reserved.

关键词： Robots

Remaining Useful Life Prediction of Bearing via a Double Attention-Based Deep Neural Network

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Remaining Useful Life Prediction of Bearing via a Double Att...

Symposia and Workshops on Ubiquitous, Autonomic and Trusted computing, UIC-ATC

作者： Yongkang Liu Donghui Pan Haifeng Zhang Kai Zhong Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Mathematical Science Anhui University Hefei Anhui China Institutes of Physical Science and Information Technology Anhui University Hefei Anhui China

Predicting the remaining useful life (RUL) of bearings is important for the secure running and reducing maintenance costs of rotating machinery. In this article, a novel feature extraction and RUL prediction framework of bearing is proposed by utilizing time-frequency representations (TFRs) and deep neural network with double attention (DA-DNN). Firstly, TFRs are employed to extract the degradation features associated with RUL prediction, which can effectively cope with the non-stationary properties of bearing vibration data. The reduced dimensional TFRs are then used as the DA-DNN model input. Afterwards, DA-DNN is developed by employing the double attention structure to extract the key degradation features more efficiently. The dual-attention structure has ability to capture the degradationrelated features from two aspects of channel attention and spatial attention, which enables the network to focus on high RUL-relevant information. Finally, the experimental results demonstrate the effectiveness of DA-DNN, which shows higher performance in terms of prediction accuracy compared to other deep learning (DL) methods.

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An Evolutionary Multi-Objective Neural Architecture Search Approach to Advancing Cognitive Diagnosis in intelligent education

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IEEE Transactions on Evolutionary Computation 2024年 1-1页

作者： Yang, Shangshang Ma, Haiping Bi, Ying Tian, Ye Zhang, Limiao Jin, Yaochu Zhang, Xingyi School of Artificial Intelligence Anhui University Hefei China Institutes of Physical Science and Information Technology Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education Anhui University Hefei China School of Electrical and Information Engineering Computational Intelligence Laboratory Zhengzhou University Zhengzhou China School of Computer Science and Technology Information Materials and Intelligent Sensing Laboratory of Anhui Province Anhui University Hefei China Information Materials and Intelligent Sensing Laboratory of Anhui Province Anhui University Hefei Anhui China School of Engineering Westlake University Hangzhou China

As a pivotal technique in intelligent education systems, cognitive diagnosis (CD) serves to reveal students’ knowledge proficiency for better tackling subsequent tasks. Unfortunately, due to pursuing high model interpretability, existing manually designed models for CD often hold simplistic architectures, which cannot cope with intricate data in modern education platforms. Furthermore, the bias of human design limits the emergence of novel and effective CD models. To develop interpretable and more effective models, thus this paper proposes an evolutionary multi-objective neural architecture search (NAS) approach for CD. Specifically, we first adopt a comprehensive search space for the NAS task of CD: all candidate models can be encompassed by a general model that deals with three distinct types of inputs. Then, an innovative model interpretability objective is devised to formulate the architecture search task as a bi-objective optimization problem (BOP). To solve the BOP, we employ a multi-objective genetic programming (MOGP) as the search strategy to explore the search space. To make the employed MOGP search well, all architectures are first encoded by trees for easy optimization, and we devise a genetic operation and a population initialization strategy to expedite its convergence. Finally, the proposed approach is actually a MOGP-based NAS approach for CD. Extensive experiments show that CD models searched by the proposed approach exhibit significantly better performance than existing models and hold as good interpretability as handcrafted models. Besides, the effectiveness of the proposed MOGP search strategy, the devised objective, and tailored strategies are validated. IEEE

关键词： Computer architecture

Surface Simulation and Design of C-band Energy Selective Surface

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Surface Simulation and Design of C-band Energy Selective Sur...

International Applied Computational Electromagnetics Society Symposium (ACES)

作者： Shangyu Lu Guohui Yang Kuang Zhang Yingsong Li School of Electronics and Information Engineering Harbin Institute of Technology Harbin China Anhui Province Key Laboratory of Target Recognition and Feature Extraction LuAn China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University China

Based on the equivalent circuit model of PIN diode and the full wave simulation method of CST software, the system performance of finite large energy selective surface (ESS) is simulated and analyzed when the number of cells is small. The simulation results show that the working performance of ESS will be degraded by the slight surface deformation caused by external force but not fail completely. Therefore, in the practical application of ESS, attention should be paid to avoid deformation caused by external force extrusion, which will reduce the shielding performance of ESS. The simulation results provide reference value for the practical design and application of energy selective surface.

关键词： Analytical models Deformation Surface waves PIN photodiodes Simulation System performance Force

Pyramid Convolution and Multi-Frequency Spatial Attention for Fine-Grained Visual Categorization

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SSRN

SSRN 2022年

作者： Xu, Qin Li, Yun Zhang, Mengquan Tao, Zhifu Luo, Bin Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Computer Science and Technology Anhui University Hefei230601 China School of Big Data and Statistics Anhui University Hefei230601 China

Learning diverse detailed feature is crucial for fine-grained visual categorization (FGVC). However, most of existing methods for FGVC use the standard convolution for feature extraction which leads to the loss of many subtle but important features. Besides, in the existing attention models for FGVC, the features are aggregated by a simple global average pooling operation, which is unable to characterize complex feature information. To address these problems, we propose pyramid convolution and multi-frequency spatial attention (PCMFSA) for FGVC. To capture spatial context dependencies of different levels and avoid the loss of the subtle features, pyramid convolution, which uses convolution kernels with various sizes, is introduced in the backbone network. To reduce the influence of background noise and obtain diverse fine-grained feature information, we propose multi-frequency spatial attention (MFSA) module, in which two channel-wise grouping operations are designed and discrete cosine transform (DCT) in the frequency domain is adopted to enhance features of different spatial positions. Moreover, to mine more valuable regions, peak suppression is used to suppress high-response regions after MFSA. A large number of experimental results show that our method achieves state-of-the-art results on four popularly FGVC datasets. © 2022, The Authors. All rights reserved.

关键词： Convolution

RGBT Tracking via Progressive Fusion Transformer with Dynamically Guided Learning

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arXiv 2023年

作者： Zhu, Yabin Li, Chenglong Wang, Xiao Tang, Jin Huang, Zhixiang Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Key Laboratory of Electromagnetic Environmental Sensing of Anhui Higher Education Institutes School of Electronic and Information Engineering Anhui University Hefei230601 China Information Materials and Intelligent Sensing Laboratory of Anhui Province Anhui Provincial Key Laboratory of Multimodal Cognitive Computation School of Artificial Intelligence Anhui University Hefei230601 China Information Materials and Intelligent Sensing Laboratory of Anhui Province Anhui Provincial Key Laboratory of Multimodal Cognitive Computation School of Computer Science and Technology Anhui University Hefei230601 China

Existing Transformer-based RGBT tracking methods either use cross-attention to fuse the two modalities, or use self-attention and cross-attention to model both modality-specific and modality-sharing information. However, the significant appearance gap between modalities limits the feature representation ability of certain modalities during the fusion process. To address this problem, we propose a novel Progressive Fusion Transformer called ProFormer, which progressively integrates single-modality information into the multimodal representation for robust RGBT tracking. In particular, ProFormer first uses a self-attention module to collaboratively extract the multimodal representation, and then uses two cross-attention modules to interact it with the features of the dual modalities respectively. In this way, the modality-specific information can well be activated in the multimodal representation. Finally, a feed-forward network is used to fuse two interacted multimodal representations for the further enhancement of the final multimodal representation. In addition, existing learning methods of RGBT trackers either fuse multimodal features into one for final classification, or exploit the relationship between unimodal branches and fused branch through a competitive learning strategy. However, they either ignore the learning of single-modality branches or result in one branch failing to be well optimized. To solve these problems, we propose a dynamically guided learning algorithm that adaptively uses well-performing branches to guide the learning of other branches, for enhancing the representation ability of each branch. Extensive experiments demonstrate that our proposed ProFormer sets a new state-of-the-art performance on RGBT210, RGBT234, LasHeR, and VTUAV datasets. In particular, the improvements of ProFormer on the LasHeR dataset are up to +6.2%/+ 4.1% in PR/SR compared with existing best RGBT tracker. Copyright © 2023, The Authors. All rights reserved.

关键词： Learning algorithms

Phase behavior of symmetric diblock copolymers under 3D soft confinement

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arXiv 2024年

作者： He, Zhijuan Huang, Jin Jiang, Kai Shi, An-Chang School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education 411105 China Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing Normal University Beijing100875 China Department of Physics and Astronomy McMaster University HamiltonONL8S 4M1 Canada

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using the self-consistent field theory. The soft confinement is realized in binary blends composed AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in the homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particle to square SL. When the C homopolymers are strongly selective to the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement. Copyright © 2024, The Authors. All rights reserved.

关键词： Free energy