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| 1 | MgNet: A unified framework of multigrid and convolutional neural network显示文摘We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model is based on close connections that we have observed and uncovered between the CNN and MG methodologies. For example, pooling operation and feature extraction in CNN correspond directly to restriction operation and iterative smoothers in MG, respectively. As the solution space is often the dual of the data space in PDEs, the analogous concept of feature space and data space (which are dual to each other) is introduced in CNN. With such connections and new concept in the unified model, the function of various convolution operations and pooling used in CNN can be better understood. As a result, modified CNN models (with fewer weights and hyperparameters) are developed that exhibit competitive and sometimes better performance in comparison with existing CNN models when applied to both CIFAR-10 and CIFAR-100 data sets. | Juncai He Jinchao Xu | 2019 | Science China Mathematics2019，62，7： | 2 |
| 2 | RELU DEEP NEURAL NETWORKS AND LINEAR FINITE ELEMENTS显示文摘In this paper,we investigate the relationship between deep neural net works(DNN)with rectified linear unit(ReLU)function as the activation function and continuous piecewise linear(CPWL)functions,especially CPWL functions from the simplicial linear finite element method(FEM).We first consider the special case of FEM.By exploring the DNN representation of its nodal basis functions,we present a ReLU DNN representation of CPWL in FEM.We theoretically establish that at least 2 hidden layers are needed in a ReLU DNN to represent any linear finite element functions inΩ■R^2 when d≥2.Consequently,for d=2,3 which are often encountered in scientific and engineering computing,the minimal number of two hidden layers are necessary and sufficient for any CPWL function to be represented by a ReLU DNN.Then we include a detailed account on how a general CPWL in R^d can be represented by a ReLU DNN with at most[log2(d+1)]|hidden layers and we also give an estimation of the number of neurons in DNN that are needed in such a represe ntation.Furthermore,using the relationship bet ween DNN and FEM,we theoretically argue that a special class of DNN models with low bit-width are still expected to have an adequate representation power in applications.Finally,as a proof of concept,we present some numerical results for using ReLU DNNs to solve a two point boundary problem to demonstrate the potential of applying DNN for numerical solution of partial differential equations. | Juncai He Lin Li Jinchao Xu Chunyue Zheng | 2020 | Journal of Computational Mathematics2020，38，3： | 2 |
| 3 | Wave propagation in water-immersed adhesive structure with the substrates of finite thickness显示文摘 | Wu Bin Ding Juncai He Cunfu | 2016 | NDT and E International2016，80，： | 1 |
| 4 | An Effective Power Optimization Approach Based on Whale Optimization Algorithm with Two-Populations and Mutation Strategies显示文摘Power is an issue that must be considered in the design of logic circuits.Power optimization is a combinatorial optimization problem,since it is necessary to search for a logical expression that consumes the least amount of power from a large number of Reed-Muller(RM)logical expressions.The existing approach for optimizing the power of multi-output mixed polarity RM(MPRM)logic circuits suffer from poor optimization results.To solve this problem,a whale optimization algorithm with two-populations strategy and mutation strategy(TMWOA)is proposed in this paper.The two-populations strategy speeds up the convergence of the algorithm by exchanging information about the two-populations.The mutation strategy enhances the ability of the algorithm to jump out of the local optimal solutions by using the information of the current optimal solution.Based on the TMWOA,we propose a multi-output MPRM logic circuits power optimization approach(TMMPOA).Experiments based on the benchmark circuits of the Microelectronics Center of North Carolina(MCNC)validate the effectiveness and superiority of the proposed TMMPOA. | Juncai HE Zhenxue HE Jia LIU Yan ZHANG Fan ZHANG Fangfang LIANG Tao WANG Limin XIAO Xiang WANG | 2024 | Chinese Journal of Electronics2024，33，2： | 0 |
| 5 | Back to Science in Searching for SARS-CoV-2 Origins显示文摘In recent decades,emerging and re-emerging human-infecting pathogens have been represented as huge threats to public health and have become a global concern(1).After outbreaks of two coronaviruses(CoVs),severe acute respiratory syndrome coronavirus(SARS-CoV)and Middle East respiratory syndrome coronavirus(MERS-CoV),severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)became the first-known pandemic hastening CoV with tremendous wrecking to the world(2).The origin tracing of these emerging pathogens is of great significance in infectious disease prevention and control(3–4).The origin of SARS-CoV-2 remains elusive after the more than 3-year pandemic,though scientists around the world are making great efforts.From the experience of studying many other infectious pathogens,origin tracing is systematic and time-consuming work.The supposed origins of many infectious pathogens are still in debate,including SARS-CoV and human immunodeficiency virus,etc(5). | William J Liu Wenwen Lei Xiaozhou He Peipei Liu Qihui Wang Zhiqiang Wu Yun Tan Shuhui Song Gary Wong Jian Lu Jingkun Jiang Qiang Wei Mingkun Li Juncai Ma Xiaozhong Peng Yixue Li Baoxu Huang Yigang Tong Jun Han Guizhen Wu | 2023 | China CDC weekly2023，5，14： | 0 |
| 6 | Bi nanoparticles encapsulated in nitrogen-doped carbon as a long-life anode material for magnesium batteries显示文摘Bismuth has garnered significant interest as an anode material for magnesium batteries(MBs) because of its high volumetric specific capacity and low working potential. Nonetheless, the limited cycling performance(≤100 cycles) limits the practical application of Bi as anode for MBs. Therefore, the improvement of Bi cycling performance is of great significance to the development of MBs and is also full of challenges. Here, Bi nanoparticles encapsulated in nitrogen-doped carbon with single-atom Bi embedded(Bi@NC) are prepared and reported as an anode material for MBs. Bi@NC demonstrates impressive performance, with a high discharge capacity of 347.5 mAh g^(-1) and good rate capability(206.4 mAh g^(-1)@500 mA g^(-1)) in a fluoride alkyl magnesium salt electrolyte. In addition, Bi@NC exhibits exceptional long-term stability, enduring 400 cycles at 500 mA g^(-1). To the best of our knowledge, among reported Bi and Bi-based compounds for MBs, Bi@NC exhibits the longest cycle life in this work. The magnesium storage mechanism of Bi@NC is deeply studied through X-ray diffraction, transmission electron microscopy and X-ray photoelectron spectroscopy. This work provides some guidance for further improving the cycling performance of other alloy anodes in MBs. | Junjun Wang Ruohan Yu Jianxiang Wang Juncai Long Fan Qiao Lei Zhang Guanjie He Qinyou An Liqiang Mai | 2023 | Journal of Magnesium and Alloys2023，11，11： | 0 |
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