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Solving Schrodinger equations using a physically constrained neural network

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Chinese Physics C 2023年第5期47卷 188-194页

作者：蒲开放李汉林吕宏亮庞龙刚 College of Science Wuhan University of Science and TechnologyWuhan 430065China HiSilicon Research Department Huawei Technologies Co.Ltd.Shenzhen 518000China Key Laboratory ofQuark and Lepton Physics(MOE)and Institute of Particle Physics Central China Normal UniversityWuhan 430079China

deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational *** a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning *** build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger *** several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low *** method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.

关键词： deep neural network auto differentiation variational problems the cumulative distribution function ground state wave function

A Survey of Accelerator Architectures for deep neural networks

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Engineering 2020年第3期6卷 264-274页

作者： Yiran Chen Yuan Xie Linghao Song Fan Chen Tianqi Tang Department of Electrical and Computer Engineering Duke UniversityDurhamNC 27708USA Department of Electrical and Computer Engineering University of CaliforniaSanta BarbaraCA 93106-9560USA

Recently,due to the availability of big data and the rapid growth of computing power,artificial intelligence(AI)has regained tremendous attention and *** learning(ML)approaches have been successfully applied to solve many problems in academia and in *** the explosion of big data applications is driving the development of ML,it also imposes severe challenges of data processing speed and scalability on conventional computer *** platforms that are dedicatedly designed for AI applications have been considered,ranging from a complement to von Neumann platforms to a“must-have”and stand-alone technical *** platforms,which belong to a larger category named“domain-specific computing,”focus on specific customization for *** this article,we focus on summarizing the recent advances in accelerator designs for deep neural networks(DNNs)-that is,DNN *** discuss various architectures that support DNN executions in terms of computing units,dataflow optimization,targeted network topologies,architectures on emerging technologies,and accelerators for emerging *** also provide our visions on the future trend of AI chip designs.

关键词： deep neural network Domain-specific architecture Accelerator

Connections between Operator-Splitting Methods and deep neural networks with Applications in Image Segmentation

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Annals of Applied Mathematics 2023年第4期39卷 406-428页

作者： Hao Liu Xue-Cheng Tai Raymond Chan Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong Norwegian Research Centre(NORCE) Nyg˚ardsgaten 1125008 BergenNorway Department of Mathematics City University of Hong Kong and Hong Kong Center for Cerebro-Cardiovascular Health EngineeringHong Kong

deep neural network is a powerful tool for many *** why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past *** the literature of mathematical analysis of deep neural networks,a lot of works is dedicated to establishing representation *** to make connections between deep neural networks and mathematical algorithms is still under *** this paper,we give an algorithmic explanation for deep neural networks,especially in their connections with operator *** show that with certain splitting strategies,operator-splitting methods have the same structure as *** this connection and the Potts model for image segmentation,two networks inspired by operator-splitting methods are *** two networks are essentially two operator-splitting algorithms solving the Potts *** experiments are presented to demonstrate the effectiveness of the proposed networks.

关键词： Potts model operator splitting deep neural network image segmentation

RELU deep neural networkS AND LINEAR FINITE ELEMENTS

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Journal of Computational Mathematics 2020年第3期38卷 502-527页

作者： Juncai He Lin Li Jinchao Xu Chunyue Zheng School of Mathematical Sciences Peking UniversityBeijing 100871China Beijing International Center for Mathematical Research Peking UniversityBeijing 100871China Department of Mathematics Pennsylvania State UniversityState CollegePA 16802USA

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 *** exploring the DNN representation of its nodal basis functions,we present a ReLU DNN representation of CPWL in *** 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≥***,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 *** 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 ***,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 ***,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.

关键词： Finite element method deep neural network Piecewise linear function

The construction of personalized virtual landslide disaster environments based on knowledge graphs and deep neural networks

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International Journal of Digital Earth 2020年第12期13卷 1637-1655页

作者： Yunhao Zhang Jun Zhu Qing Zhu Yakun Xie Weilian Li Lin Fu Junxiao Zhang Jianmei Tan Faculty of Geosciences and Environmental Engineering Southwest Jiaotong UniversityChengduSichuanPeople’s Republic of China China Mobile Communications Sichuan Group Co. LtdChengduSichuanPeople’s Republic of China

Virtual Landslide Disaster environments are important for multilevel simulation,analysis and decision-making about Landslide ***,in the existing related studies,complex disaster scene objects and relationships are not deeply analyzed,and the scene contents are fixed,which is not conducive to meeting multilevel visualization task requirements for diverse *** resolve the above issues,a construction method for Personalized Virtual Landslide Disaster Environments Based on Knowledge Graphs and deep neural networks is proposed in this *** characteristics of relationships among users,scenes and data were first discussed in detail;then,a knowledge graph of virtual Landslide Disaster environments was established to clarify the complex relationships among disaster scene objects,and a deep neural network was introduced to mine the user history information and the relationships among object entities in the knowledge ***,a personalized Landslide Disaster scene data recommendation mechanism was ***,a prototype system was developed,and an experimental analysis was *** experimental results show that the method can be used to recommend intelligently appropriate disaster information and scene data to diverse *** recommendation accuracy stabilizes above 80%–a level able to effectively support The Construction of Personalized Virtual Landslide Disaster environments.

关键词： Landslide disaster scene virtual disaster environment knowledge graph deep neural network personalized recommendation

Optimization-inspired manual architecture design and neural architecture search

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Science China(Information Sciences) 2023年第11期66卷 100-112页

作者： Yibo YANG Zhengyang SHEN Huan LI Zhouchen LIN JD Explore Academy School of Mathematical Sciences Peking University Institute of Robotics and Automatic Information Systems College of Artificial Intelligence Nankai University Key Lab of General Artificial Intelligence School of Intelligence Science and Technology Peking University Institute for Artificial Intelligence Peking University Pazhou Lab

neural architecture has been a research focus in recent years due to its importance in deciding the performance of deep networks. Representative ones include a residual network(Res Net) with skip connections and a dense network(Dense Net) with dense connections. However, a theoretical guidance for manual architecture design and neural architecture search(NAS) is still lacking. In this paper, we propose a manual architecture design framework, which is inspired by optimization algorithms. It is based on the conjecture that an optimization algorithm with a good convergence rate may imply a neural architecture with good performance. Concretely, we prove under certain conditions that forward propagation in a deep neural network is equivalent to the iterative optimization procedure of the gradient descent algorithm minimizing a cost function. Inspired by this correspondence, we derive neural architectures from fast optimization algorithms,including the heavy ball algorithm and Nesterov’s accelerated gradient descent algorithm. Surprisingly, we find that we can deem the Res Net and Dense Net as special cases of the optimization-inspired *** architectures offer not only theoretical guidance, but also good performances in image recognition on multiple datasets, including CIFAR-10, CIFAR-100, and Image Net. Moreover, we show that our method is also useful for NAS by offering a good initial search point or guiding the search space.

关键词： deep neural network manual architecture design neural architecture search image recognition optimization algorithms learning-based optimization

Federated learning based QoS-aware caching decisions in fog-enabled internet of things networks

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Digital Communications and networks 2023年第2期9卷 580-589页

作者： Xiaoge Huang Zhi Chen Qianbin Chen Jie Zhang School of Communication and Information Engineering Chongqing University of Post and TelecommunicationsChongqing400065China School of Communication and Information Engineering University of SheffieldUnited Kingdom

Quality of Service(QoS)in the 6G application scenario is an important issue with the premise of the massive data *** caching based on the fog computing network is considered as a potential solution to effectively reduce the content fetch delay for latency-sensitive services of Internet of Things(IoT)*** the time-varying scenario,the machine learning techniques could further reduce the content fetch delay by optimizing the caching *** this paper,to minimize the content fetch delay and ensure the QoS of the network,a Device-to-Device(D2D)assisted fog computing network architecture is introduced,which supports federated learning and QoS-aware caching decisions based on time-varying user *** release the network congestion and the risk of the user privacy leakage,federated learning,is enabled in the D2D-assisted fog computing ***,it has been observed that federated learning yields suboptimal results according to the Non-Independent Identical Distribution(Non-IID)of local users *** address this issue,a distributed cluster-based user preference estimation algorithm is proposed to optimize the content caching placement,improve the cache hit rate,the content fetch delay and the convergence rate,which can effectively mitigate the impact of the Non-IID data set by *** simulation results show that the proposed algorithm provides a considerable performance improvement with better learning results compared with the existing algorithms.

关键词： Fog computing network IoT D2D communication deep neural network Federated learning

Plasmonic nanostructure characterized by deep-neuralnetwork-assisted spectroscopy[Invited]

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Chinese Optics Letters 2023年第1期21卷 17-24页

作者：董奇奥王文琦曹欣怡肖依博郭笑涵马敬轩汪联辉高丽 State Key Laboratory for Organic Electronics and Information Displays Institute of Advanced MaterialsSchool of Materials Science and EngineeringNanjing University of Posts and TelecommunicationsNanjing 210023China

The lateral geometry and material property of plasmonic nanostructures are critical parameters for tailoring their optical resonance for sensing *** lateral geometry can be easily observed by a scanning electron microscope or an atomic force microscope,characterizing materials properties of plasmonic devices is not straightforward and requires delicate examination of material composition,cross-sectional thickness,and refractive *** this study,a deep neural network is adopted to characterize these parameters of unknown plasmonic nanostructures through simple transmission *** network architecture is established based on simulated data to achieve accurate identification of both geometric and material *** then demonstrate that the network training by a mixture of simulated and experimental data can result in correct material property *** work may indicate a simple and intelligent characterization approach to plasmonic nanostructures by spectroscopic techniques.

关键词： plasmonics soft nanoimprint lithography deep neural network nanostructure characterization

An online fast multi-track locating algorithm for high-resolution single-event effect test platform

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Nuclear Science and Techniques 2023年第5期34卷 86-100页

作者： Yu-Xiao Hu Hai-Bo Yang Hong-Lin Zhang Jian-Wei Liao Fa-Tai Mai Cheng-Xin Zhao Institute of modern physics Chinese Academy of SciencesLanzhou 730000China Advanced Energy Science and Technology Guangdong Laboratory Huizhou 516003China University of Chinese Academy of Sciences Beijing 100049China

To improve the efficiency and accuracy of single-event effect(SEE)research at the Heavy Ion Research Facility at Lanzhou,Hi’Beam-SEE must precisely localize the position at which each heavy ion hitting the integrated circuit(IC)causes *** this study,we propose a fast multi-track location(FML)method based on deep learning to locate the position of each particle track with high speed and *** can process a vast amount of data supplied by Hi’Beam-SEE online,revealing sensitive areas in real *** is a slot-based object-centric encoder-decoder structure in which each slot can learn the location information of each track in the *** make the method more accurate for real data,we designed an algorithm to generate a simulated dataset with a distribution similar to that of the real data,which was then used to train the *** comparison experiments demonstrated that the FML method,which has the best performance on simulated datasets,has high accuracy on real datasets as *** particular,FML can reach 238 fps and a standard error of 1.6237μ*** study discusses the design and performance of FML.

关键词： Beam tracks Multi-track location Rapid location High accuracy Synthetic data deep neural network Single-event effects Silicon pixel sensors HIRFL