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Pass-Efficient randomized lu algorithms for computing low-rank matrix approximation

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arXiv 2020年

作者： Zhang, Bolong Mascagniy, Michael Department of Computer Science Florida State University FL United States Applied and Computational Mathematics Division NIST GaithersburgMD United States

Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such as singular value decomposition (SVD) and column pivoting QR decomposition (CPQR), are either prohibitively expensive or cannot provide sufficiently accurate results. A solution is to use randomized low-rank matrix approximation methods such as randomized SVD , and randomized LU decomposition on extremely large data sets. In this paper, we focus on the randomized LU decomposition method. First, we employ a reorthogonalization procedure to perform the power iteration of the existing randomized LU algorithm to compensate for the rounding errors caused by the power method. Then we propose a novel randomized LU algorithm, called PowerLU, for the fixed low-rank approximation problem. PowerLU allows for an arbitrary number of passes of the input matrix, v = 2. Recall that the existing randomized LU decomposition only allows an even number of passes. We prove the theoretical relationship between PowerLU and the existing randomized LU. Numerical experiments show that our proposed PowerLU is generally faster than the existing randomized LU decomposition, while remaining accurate. We also propose a version of PowerLU, called PowerLU FP, for the fixed precision low-rank matrix approximation problem. PowerLU FP is based on an efficient blocked adaptive rank determination Algorithm 4.1 proposed in this paper. We present numerical experiments that show that PowerLU FP can achieve almost the same accuracy and is faster than the randomized blocked QB algorithm by Martinsson and Voronin. We finally propose a single-pass algorithm based on LU factorization. Tests show that the accuracy of our single-pass algorithm is comparable with the existing single-pass *** Codes 65F99, 65C99 Copyright © 2020, The Authors. All rights reserved.

关键词： Singular value decomposition

Extending the limit of molecular dynamics with ab initio accuracy to 10 billion atoms

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arXiv 2022年

作者： Guo, Zhuoqiang Lu, Denghui Yan, Yujin Hu, Siyu Liu, Rongrong Tan, Guangming Sun, Ninghui Jiang, Wanrun Liu, Lijun Chen, Yixiao Zhang, Linfeng Chen, Mohan Wang, Han Jia, Weile Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Architecture ICT Chinese Academy of Sciences Beijing China HEDPS CAPT College of Engineering Peking University Beijing China AI for Science Institute Beijing China Osaka University Osaka Japan Princeton University Princeton United States DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

High-performance computing, together with a neural network model trained from data generated with first-principles methods, has greatly boosted applications of ab initio molecular dynamics in terms of spatial and temporal scales on modern supercomputers. Previous state-of-the-art can achieve 1 − 2 nanoseconds molecular dynamics simulation per day for 100-million atoms on the entire Summit supercomputer. In this paper, we have significantly reduced the memory footprint and computational time by a comprehensive approach with both algorithmic and system innovations. The neural network model is compressed by model tabulation, kernel fusion, and redundancy removal. Then optimizations such as acceleration of customized kernel, tabulation of activation function, MPI+OpenMP parallelization are implemented on GPU and ARM architectures. Testing results of the copper system show that the optimized code can scale up to the entire machine of both Fugaku and Summit, and the corresponding system size can be extended by a factor of 134 to an © 2022, CC BY-NC-SA.

关键词： Supercomputers

Deoscillated adaptive graph collaborative filtering

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arXiv 2020年

作者： Liu, Zhiwei Meng, Lin Jiang, Fei Zhang, Jiawei Yu, Philip S. Department of Computer Science University of Illinois Chicago United States Department of Computer Science Florida State University United States Committee on Computational and Applied Mathematics University of Chicago United States

Collaborative Filtering (CF) signals are crucial for a Recommender System (RS) model to learn user and item embeddings. High-order information can alleviate the cold-start issue of CF-based methods, which is modeled through propagating the information over the user-item bipartite graph. Recent Graph Neural Networks (GNNs) propose to stack multiple aggregation layers to propagate high-order signals. However, there are three challenges, the oscillation problem, varying locality of bipartite graph, and the fixed propagation pattern, which spoil the ability of the multilayer structure to propagate information. In this paper, we theoretically prove the existence and boundary of the oscillation problem, and empirically study the varying locality and layer-fixed propagation problems. We propose a new RS model, named as Deoscillated adaptive Graph Collaborative Filtering (DGCF), which is constituted by stacking multiple CHP layers and LA layers. We conduct extensive experiments on real-world datasets to verify the effectiveness of DGCF. Detailed analyses indicate that DGCF solves oscillation problems, adaptively learns local factors, and has layer-wise propagation patterns. Our code is available online. Copyright © 2020, The Authors. All rights reserved.

关键词： Collaborative filtering

A class of elliptic mixed boundary value problems with (p,q)-Laplacian: existence, comparison and optimal control

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arXiv 2023年

作者： Zeng, Shengda Migórski, Stanislaw Tarzia, Domingo A. Zou, Lang Nguyen, Van Thien Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin537000 China Department of Mathematics Nanjing University Jiangsu Nanjing210093 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30348 Poland College of Applied Mathematics Chengdu University of Information Technology Sichuan Province Chengdu610225 China Jagiellonian University in Krakow Chair of Optimization and Control ul. Lojasiewicza 6 Krakow30348 Poland Depto. Matemática FCE Universidad Austral Paraguay 1950 RosarioS2000FZF Argentina CONICET Argentina School of Mathematics and Computational Science Xiangtan University Hunan Province Xiangtan City210000 China Department of Mathematics FPT University Education zone Hoa Lac High Tech Park Km29 Thang Long Highway Thach That ward Hanoi Viet Nam

The paper deals with two nonlinear elliptic equations with (p, q)-Laplacian and the Dirichlet-Neumann-Dirichlet (DND) boundary conditions, and Dirichlet-Neumann-Neumann (DNN) boundary conditions, respectively. Under mild hypotheses, we prove the unique weak solvability of the elliptic mixed boundary value problems. Then, a comparison and a monotonicity results for the solutions of elliptic mixed boundary value problems are established. We examine a convergence result which shows that the solution of (DND) can be approached by the solution of (DNN). Moreover, two optimal control problems governed by (DND) and (DNN), respectively, are considered, and an existence result for optimal control problems is obtained. Finally, we provide a result on asymptotic behavior of optimal controls and system states, when a parameter tends to *** Codes 35J25, 35J66, 35J92, 49J20, 35Bxx © 2023, CC BY.

关键词： Nonlinear equations

Reinforcement Learning reveals fundamental limits on the mixing of active particles

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arXiv 2021年

作者： Schildknecht, Dominik Popova, Anastasia N. Stellwagen, Jack Thomson, Matt Biology and Biological Engineering California Institute of Technology PasadenaCA91125 United States Applied and Computational Mathematics California Institute of Technology PasadenaCA91125 United States School of Computer Science Carnegie Mellon University PittsburghPA15213 United States

The control of far-from-equilibrium physical systems, including active materials, has emerged as an important area for the application of reinforcement learning (RL) strategies to derive control policies for physical systems. In active materials, non-linear dynamics and long-range interactions between particles prohibit closed-form descriptions of the system's dynamics and prevent explicit solutions to optimal control problems. Due to fundamental challenges in solving for explicit control strategies, RL has emerged as an approach to derive control strategies for far-from-equilibrium active matter systems. However, an important open question is how the mathematical structure and the physical properties of the active matter systems determine the tractability of RL for learning control policies. In this work, we show that RL can only find good strategies to the canonical active matter task of mixing for systems that combine attractive and repulsive particle interactions. Using mathematical results from dynamical systems theory, we relate the availability of both interaction types with the existence of hyperbolic dynamics and the ability of RL to find homogeneous mixing strategies. In particular, we show that for drag-dominated translational-invariant particle systems, hyperbolic dynamics and, therefore, mixing requires combining attractive and repulsive interactions. Broadly, our work demonstrates how fundamental physical and mathematical properties of dynamical systems can enable or constrain reinforcement learning-based control. Copyright © 2021, The Authors. All rights reserved.

关键词： Mixing

DPA-2:a large atomic model as a multitask learner

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npj computational Materials 2024年第1期10卷 185-199页

作者： Duo Zhang Xinzijian Liu Xiangyu Zhang Chengqian Zhang Chun Cai Hangrui Bi Yiming Du Xuejian Qin Anyang Peng Jiameng Huang Bowen Li Yifan Shan Jinzhe Zeng Yuzhi Zhang Siyuan Liu Yifan Li Junhan Chang Xinyan Wang Shuo Zhou Jianchuan Liu Xiaoshan Luo Zhenyu Wang Wanrun Jiang Jing Wu Yudi Yang Jiyuan Yang Manyi Yang Fu-Qiang Gong Linshuang Zhang Mengchao Shi Fu-Zhi Dai Darrin M.York Shi Liu Tong Zhu Zhicheng Zhong Jian Lv Jun Cheng Weile Jia Mohan Chen Guolin Ke Weinan E Linfeng Zhang Han Wang AI for Science Institute BeijingP.R.China DP Technology BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking UniversityBeijingP.R.China State Key Lab of Processors Institute of Computing TechnologyChinese Academy of SciencesBeijingP.R.China University of Chinese Academy of Sciences BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingP.R.China Ningbo Institute of Materials Technology and Engineering Chinese Academy of SciencesNingboP.R.China CAS Key Laboratory of Magnetic Materials and Devices and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of SciencesNingboP.R.China School of Electronics Engineering and Computer Science Peking UniversityBeijingP.R.China Shanghai Engineering Research Center of Molecular Therapeutics&New Drug Development School of Chemistry and Molecular EngineeringEast China Normal UniversityShanghaiP.R.China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine and Department of Chemistry and Chemical BiologyRutgers UniversityPiscatawayNJUSA Department of Chemistry Princeton UniversityPrincetonNJUSA College of Chemistry and Molecular Engineering Peking UniversityBeijingP.R.China Yuanpei College Peking UniversityBeijingP.R.China School of Electrical Engineering and Electronic Information Xihua UniversityChengduP.R.China State Key Laboratory of Superhard Materials College of PhysicsJilin UniversityChangchunP.R.China Key Laboratory of Material Simulation Methods&Software of Ministry of Education College of PhysicsJilin UniversityChangchunP.R.China International Center of Future Science Jilin UniversityChangchunP.R.China Key Laboratory for Quantum Materialsof Zhejiang Province Department of PhysicsSchool of ScienceWestlake UniversityHangzhouP.R.China Atomistic Simulations Italian Institute of TechnologyGenovaItaly State Key Laboratory of Physical Chemistry of Solid Surface iChEMCollege of Chemistry and Chemical EngineeringXiame

The rapid advancements in artificial intelligence(AI)are catalyzing transformative changes in atomic modeling,simulation,and ***-driven potential energy models havedemonstrated the capability to conduct large-scale,long-duration simulations with the accuracy of ab initio electronic structure ***,the model generation process remains a bottleneck for large-scale *** propose a shift towards a model-centric ecosystem,wherein a large atomic model(LAM),pretrained across multiple disciplines,can be efficiently fine-tuned and distilled for various downstream tasks,thereby establishing a new framework for molecular *** this study,we introduce the DPA-2 architecture as a prototype for ***-trained on a diverse array of chemical and materials systemsusing a multi-task approach,DPA-2demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning *** approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research.

关键词： DPA establishing thereby

Strong solutions of the equations for Viscoelastic fluids in some classes of large data

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arXiv 2020年

作者： Jiang, Fei Jiang, Song College of Mathematics and Computer Science Fuzhou University Fuzhou350108 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

We study the existence and uniqueness of global strong solutions to the equations of an incompressible viscoelastic fluid in a spatially periodic domain, and show that a unique strong solution exists globally in time if the initial deformation and velocity are small for the given physical parameters. In particular, the initial velocity can be large for the large elasticity coefficient. The result of this paper mathematically verifies that the elasticity can prevent the formation of singularities of strong solutions with large initial velocity, thus playing a similar role to viscosity in preventing the formation of singularities in viscous flows. Moreover, for given initial velocity perturbation and zero initial deformation around the rest state, we find, as the elasticity coefficient or time go to infinity, that (1) any straight line segment l0 consisted of ﬂuid particles in the rest state, after being bent by a velocity perturbation, will turn into a straight line segment that is parallel to l0 and has the same length as l0 (see Remark 1.3). (2) the motion of the viscoelastic ﬂuid can be approximated by a linear pressureless motion in Lagrangian coordinates, even when the initial velocity is ***, the above mentioned phenomena can also be found in the corresponding compressible fluid case. Copyright © 2020, The Authors. All rights reserved.

关键词： Deformation

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

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arXiv 2024年

作者： Hirsbrunner, Mark R. Mullinax, J. Wayne Shen, Yizhi Williams-Young, David B. Klymko, Katherine Van Beeumen, Roel Tubman, Norm M. Department of Physics University of Illinois at Urbana-Champaign UrbanaIL61801 United States USRA Research Institute for Advanced Computer Science Mountain ViewCA94043 United States KBR Inc. NASA Ames Research Center Moffett FieldCA94035 United States Intelligent Systems Division NASA Ames Research Center Moffett FieldCA94035 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States NERSC Lawrence Berkeley National Lab BerkeleyCA94720 United States

Recent research has shown that wavefunction evolution in real- and imaginary-time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at a local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima. © 2024, CC BY-NC-SA.

关键词： Ground state

Periodicity Scoring of Time Series Encodes Dynamical Behavior of the Tumor Suppressor p53 ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 488-495页

作者： Caroline Moosmüller Christopher J. Tralie Mahdi Kooshkbaghi Zehor Belkhatir Maryam Pouryahya José Reyes Joseph O. Deasy Allen R. Tannenbaum Ioannis G. Kevrekidis C. Moosmüller and C. Tralie contributed equally to this work Department of Mathematics University of California San Diego La Jolla CA 92093 USA Department of Medical Physics Memorial Sloan-Kettering Cancer Center NY USA Department of Chemical and Biomolecular Engineering Johns Hopkins University Baltimore MD 21218 USA Department of Mathematics and Computer Science Ursinus College Collegeville PA USA Program in Applied and Computational Mathematics Princeton University NJ USA School of Engineering and Sustainable Development De Montfort University Leicester UK Cancer Biology and Genetics Program and Computational and Systems Biology Program Memorial Sloan-Kettering Cancer Center New York NY 10065 USA and Department of Systems Biology Harvard Medical School Boston MA 02115 USA Departments of Computer Science and Applied Mathematics & Statistics Stony Brook University NY USA

In this paper we analyze the dynamical behavior of the tumor suppressor protein p53, an essential player in the cellular stress response, which prevents a cell from dividing if severe DNA damage is present. When this response system is malfunctioning, e.g. due to mutations in p53, uncontrolled cell proliferation may lead to the development of cancer. Understanding the behavior of p53 is thus crucial to prevent its failing. It has been shown in various experiments that periodicity of the p53 signal is one of the main descriptors of its dynamics, and that its pulsing behavior (regular vs. spontaneous) indicates the level and type of cellular stress. In the present work, we introduce an algorithm to score the local periodicity of a given time series (such as the p53 signal), which we call Detrended Autocorrelation Periodicity Scoring (DAPS). It applies pitch detection (via autocorrelation) on sliding windows of the entire time series to describe the overall periodicity by a distribution of localized pitch scores. We apply DAPS to the p53 time series obtained from single cell experiments and establish a correlation between the periodicity scoring of a cell’s p53 signal and the number of cell division events. In particular, we show that high periodicity scoring of p53 is correlated to a low number of cell divisions and vice versa. We show similar results with a more computationally intensive state-of-the-art periodicity scoring algorithm based on topology known as Sw1PerS. This correlation has two major implications: It demonstrates that periodicity scoring of the p53 signal is a good descriptor for cellular stress, and it connects the high variability of p53 periodicity observed in cell populations to the variability in the number of cell division events.

关键词： Systems biology cellular systems time series modeling bioinformatics computational biology