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arXiv 2024年

作者： Chen, Huangxin Dong, Piaopiao Wang, Dong Wang, Xiao-Ping School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian361005 China School of Science and Engineering The Chinese University of Hong Kong Guangdong Shenzhen518172 China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data Guangdong518172 China

In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM. Copyright © 2024, The Authors. All rights reserved.

关键词： Convolution

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A Prediction-Correction Based Iterative Convolution-Thresholding Method for Topology Optimization of Heat Transfer Problems

SSRN

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SSRN 2024年

关键词： Convolution

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Precise and scalable evaluation on the robustness metric of neural networks as classifiers

Precise and scalable evaluation on the robustness metric of ...

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作者： Yangyi Hu Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense Technology College of Computer Science National University of Defense Technology

It is well known that the minimum adversarial distortion associated with a specific sample x reflects the local robustness of neural ***,it is intractable to solve the optimization problem related to the minimum adversarial distortion for general neural network cause it is *** have studied the lower bound or upper bound of the minimum adversarial distortion to give a robustness metrics for neural networks,such as CLEVER score and CW *** this paper,we provide a formal robustness guarantee to transform the robustness analysis into two sub-problems:（1）,compute out the maximum of the objective function g_t（r~t）;（2）,generate a sequence {r_n~t} *** r_n~t is the minimum adversarial distortion for targeted *** on this transformation,we propose an efficient and effective algorithm to directly estimate the instance-specific minimum adversarial distortion on the norm of the input manipulation required to change the classifier *** results on two data-sets,MNIST and CIFAR,show that our measure of robustness is between the lower bound given by CLEVER and the upper bound by CW,indicating our approach gives a precise measure of the robustness of neural *** addition,the powerful mathematical technique Extreme Value Estimation enables our algorithm computationally feasible for large neural *** the best of our knowledge,our algorithm is the first attack-independent approach to directly evaluate the minimum adversarial distortion as a robustness metric for neural network.

关键词： minimum adversarial distortion robustness metric instance-specific attack-independent

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Explicitly represent the boundary of ReLU NN as a classifier and measure its robustness

Explicitly represent the boundary of ReLU NN as a classifier...

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Adversarial examples pose a great threat to the application of neural network as a classifier in areas with high security ***,the adversarial property of neural network is closely related to the ***,works barely give a rigorous description of *** paper for the first time studies the boundary of ReLU NN,which separates the sample space into distinct cells,each of which belongs to the same *** the demonstration,we discuss the algebraic property of border points upon the separating boundary and the topological difference between border points and odd *** derive Theorem Ⅲ.7 to give a rigorous,comprehensive and concise description on the boundary of ReLU ***,an algorithm,based on the description,is proposed to give a standard and exact metric for the local robustness of ReLU *** metric gives the local adversarial property of NN and reflects some aspects of its security performance,*** nimimum distortion needed to craft an adversarial *** the best of our knowledge,this is the first work proposed to give a rigorous and example-specific metric for the local robustness of ReLU NN.

关键词： Index Terms-adversarial examples boundary odd points local robustness metric

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Solving high-dimensional Parametric Elliptic Equation Using Tensor Neural Network

arXiv

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arXiv 2024年

作者： Chen, Hongtao Fu, Rui Wang, Yifan Xie, Hehu School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen361005 China LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences No.55 Zhongguancun Donglu Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we can transform the high-dimensional integrations of tensor neural network functions to one-dimensional integrations which can be computed with the classical quadrature schemes with high accuracy. The complexity of its calculation can be reduced from the exponential scale to a polynomial scale. The corresponding machine learning method is designed for solving high-dimensional parametric elliptic equations. Some numerical examples are provided to validate the accuracy and efficiency of the proposed *** Codes 35B27, 60H15, 60H35, 68T07 © 2024, CC0.

关键词： Tensors

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Detection of a new GeV source in the outer region of the Coma cluster: a signature of external accretion shock ?

arXiv

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arXiv 2024年

作者： Chen, Xiao-Bin Wang, Kai Huang, yi-Yun Zhang, Hai-Ming Xi, Shao-Qiang Liu, Ruo-Yu Wang, Xiang-Yu School of Astronomy and Space Science Nanjing University Nanjing210023 China Ministry of Education Nanjing210023 China Guangxi Key Laboratory for Relativistic Astrophysics School of Physical Science and Technology Guangxi University Nanning530004 China Key Laboratory of Particle Astrophysics & Experimental Physics Division & Computing Center Institute of High Energy Physics Chinese Academy of Sciences Beijing100049 China

The supersonic flow motions associated with infall of baryonic gas toward sheets and filaments, as well as cluster mergers, produces large-scale shock waves. The shocks associated with galaxy clusters can be classified mainly into two categories: internal shocks appear in the hot intracluster medium within the viral radius, and external accretion shocks form in the outer cold region well outside of the virial radius. Cosmic-ray (CR) electrons and/or protons accelerated by these shocks are expected to produce gamma-rays through inverse-Compton scatterings (ICS) or inelastic pp collisions respectively. Recent studies have found a spatially extended GeV source within the virial radius, consistent with the internal shock origin. Here we report the detection of a new GeV source at a distance of about 2.8◦ from the center of the Coma cluster through the analysis of 16.2 years of Fermi-LAT data. The hard spectrum of the source, in agreement with the ICS origin, and its location in a large-scale filament of galaxies points to the external accretion shock origin. The gamma-ray (0.1 − 103 GeV) luminosity of the source, 1.4 × 1042 erg s−1, suggests that a fraction ∼ 10−3 of the kinetic energy flux through the shock-surface is transferred to relativistic CR electrons. © 2024, CC BY.

关键词： Cosmic rays

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Printed thin film transistors with 10^(8)on/off ratios and photoelectrical synergistic characteristics using isoindigo-based polymers-enriched(9,8)carbon nanotubes

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Nano Research 2022年第6期15卷 5517-5526页

作者： Wenjing Xu Min Li Masayoshi Tange Liqiang Li Juncai Hou Jun Ye Li Wei Yuan Chen Jianwen Zhao School of Materials Science and Engineering Shaanxi University of TechnologyHanzhong 723001China Division of Nanodevices and Related Nanomaterials Printable Electronics Research CentreSuzhou Institute of Nano-Tech and Nano-BionicsChinese Academy of SciencesNo.398 Ruoshui RoadSEIDSuzhou Industrial ParkSuzhou 215123China School of Nano Technology and Nano Bionics University of Science and Technology of ChinaHefei 230026China National and Local Joint Engineering Laboratory for Slag Comprehensive Utilization and Environmental Technology Shaanxi University of TechnologyHanzhong 723001China Nanomaterials Research Institute National Institute of Advanced Industrial Science and Technology(AIST)Tsukuba 3058565Japan Advanced Materials Division Suzhou Institute of Nano-Tech and Nano-BionicsChinese Academy of SciencesNo.398 Ruoshui RoadSEIDSuzhou Industrial ParkSuzhou 215123China Institute of High Performance Computing Agency for ScienceTechnology and ResearchSingapore 138632Singapore School of Chemical and Biomolecular Engineering The University of SydneyCamperdownNSW 2006Australia

Monochiral single-walled carbon nanotubes(SWCNTs)can enable high-performance carbon-based electronic devices and integrated ***,their fabrication often requires complex SWCNT purification and ***,we showed that isoindigo-based polymer derivatives(PDPPIID and PFIID)directly enriched(9,8)nanotubes from as-synthesized SWCNT powders selectively and efficiently to yield high concentration(9,8)nanotube *** selective wrapping mechanism was elucidated by classical full-atomistic molecular dynamic(MD)***-film transistors(TFTs)were fabricated by depositing the SWCNT ink into device channels using aerosol jet *** performance was strongly influenced by polymer residues,the deposition condition(humidity),and ink *** TFTs showed excellent device-to-device uniformity with 108 on/off ***,optoelectronic transistors were fabricated,and their photoelectrical neuromorphic characteristics,storage,memory,and logic functions were characterized under the pulsed light and voltage stimulations,demonstrating excellent application potentials.

关键词： monochiral carbon nanotube polymer wrapping printed thin-film transistor photoelectrical synergistic molecular dynamic simulation

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Kernel neural operator for efficient solving PDEs

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AIP Conference Proceedings 2024年第1期3094卷

作者： Bao Kaijun Qian Xu Liu Ziyuan Wang Haifeng Song Songhe College of Science National University of Defense Technology Changsha 410073 China State Key Laboratory of High Performance Computing National University of Defense Technology Changsha 410073 China

Recently, the development of neural networks for solving partial differential equations (PDEs) has been extended to neural operators, which directly learn the mapping from any functional parametric dependence to the solution. Thus, compared to classical numerical methods, neural operators demonstrate the advantage in solving a family of PDEs. Motivated by recently successful neural operator: Fourier neural operator (FNO), we design a novel neural operator based on the encoder-decoder frame- work and the general integral operator whose kernel function is represented by the kernel method. Comparing to FNO, the proposed model allows for an expressive and efficient architecture, which greatly reduces the number of parameters and also has desirable results on numerical experiments.

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MDENet: Multi-modal Dual-embedding Networks for Malware Open-set Recognition

arXiv

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arXiv 2023年

作者： Guo, Jingcai Xu, Yuanyuan Xu, Wenchao Zhan, Yufeng Sun, Yuxia Guo, Song Department of Computing The Hong Kong Polytechnic University Hong Kong The Hong Kong Polytechnic University Shenzhen Research Institute Shenzhen518057 China School of Information and Software Engineering University of Electronic Science and Technology of China Chengdu610054 China School of Automation Beijing Institute of Technology Beijing100081 China Department of Computer Science Jinan University Guangzhou510632 China Guangdong Provincial Key Laboratory of High-Performance Computing Guangzhou510275 China

Malware open-set recognition (MOSR) aims at jointly classifying malware samples from known families and detect the ones from novel unknown families, respectively. Existing works mostly rely on a well-trained classifier considering the predicted probabilities of each known family with a threshold-based detection to achieve the MOSR. However, our observation reveals that the feature distributions of malware samples are extremely similar to each other even between known and unknown families. Thus the obtained classifier may produce overly high probabilities of testing unknown samples toward known families and degrade the model performance. In this paper, we propose the Multi-modal Dual-Embedding Networks, dubbed MDENet, to take advantage of comprehensive malware features from different modalities to enhance the diversity of malware feature space, which is more representative and discriminative for down-stream recognition. Concretely, we first generate a malware image for each observed sample based on their numeric features using our proposed numeric encoder with a re-designed multi-scale CNN structure, which can better explore their statistical and spatial correlations. Besides, we propose to organize tokenized malware features into a sentence for each sample considering its behaviors and dynamics, and utilize language models as the textual encoder to transform it into a representable and computable textual vector. Such parallel multi-modal encoders can fuse the above two components to enhance the feature diversity. Last, to further guarantee the open-set recognition, we dually embed the fused multi-modal representation into one primary space and an associated subspace, i.e., discriminative and exclusive spaces, with contrastive sampling and ρ-bounded enclosing sphere regularizations, which resort to classification and detection, respectively. Moreover, we also enrich our previously proposed large-scaled malware dataset MAL-100 with multi-modal characteristics and cont

关键词： Modal analysis

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Predicting Quantum Many-Body Dynamics with Transferable Neural Net works

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Chinese Physics Letters 2020年第1期37卷 101-104页

作者： Ze-Wang Zhang Shuo Yang Yi-Hang Wu Chen-Xi Liu Yi-Min Han Ching-Hua Lee Zheng Sun Guang-Jie Li Xiao Zhang School of Physics Sun Yat-sen UniversityGuangzhou 510275 State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics Tsinghua UniversityBeijing 100084 Department of Physics National University of Singapore117542Singapore Institute of High Performance Computing 138632Singapore

Advanced machine learning(ML)approaches such as transfer learning have seldom been applied to approximate quantum many-body *** we demonstrate that a simple recurrent unit(SRU)based efficient and transferable sequence learning framework is capable of learning and accurately predicting the time evolution of the one-dimensional(ID)Ising model with simultaneous transverse and parallel magnetic fields,as quantitatively corroborated by relative entropy measurements between the predicted and exact state *** a cost of constant computational complexity,a larger many-body state evolution is predicted in an autoregressive way from just one initial state,without any guidance or knowledge of any *** work paves the way for future applications of advanced ML methods in quantum many-body dynamics with knowledge only from a smaller system.

关键词： quantum exact entropy

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