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Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs

Science China Mathematics 2010年第1期53卷 1-22页

作者： WANG Bo1,WANG Rui2 & XU YueSheng3,4,1Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China 2School of Information Science and Engineering,Graduate University of the Chinese Academy of Sciences,Beijing 100190,China 3department of Mathematics,Syracuse University,Syracuse,NY 13244,USA 4department of scientific computing and computer applications,Sun Yat-sen University,Guangzhou 510275,China 1. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. School of Information Science and Engineering Graduate University of the Chinese Academy of Sciences Beijing 100190 China3. Department of Mathematics Syracuse University Syracuse NY 13244 USA4. Department of Scientific Computing and Computer Applications Sun Yat-sen University Guangzhou 510275 China

We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the *** optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is *** this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the *** examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.

关键词： Dirichlet problem open arc singular boundary integral equations Fourier-Galerkin methods logarithmic potentials

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Deep Learning Based Automated Electronic Meter Reading System using YOLOv5 Architecture 23

Deep Learning Based Automated Electronic Meter Reading Syste...

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Proceedings of the 2023 International Conference on Big Data Mining and Information Processing

作者： Harsh Gupta Ankita Jaiswal Pavinder Yadav Nidhi Gupta Department of Mathematics and Scientific Computing National Institute of Technology India Department of Mechanical Engineering National Institute of Technology India Department of Computer Applications National Institute of Technology India

ISBN: (纸本)9798400709166

Automatic instrument reading has become a critical issue for intelligent sensors in smart cities. Several artificial intelligence techniques are developing tools for addressing the issue. The image-based Automatic Meter Reading (AMR) techniques have been tested on images taken under regulated conditions, but they become unresponsive when dealing with fuzzy, hazy or blurred meter images. In this paper, we deal with AMR, which focuses on unconstrained settings such as fuzzy, hazy or blurry meter images. Automated meter reading consists of three major components: identifying the counter region, localising and cropping the counter region and digit recognition. In this article, the deep learning model YOLOv5 have been used on the image dataset. YOLOv5 is a state-of-the-art single-stage deep learning detector that outperforms all other detectors and it is observed that the proposed technique and the trained model based on YOLOv5 can reliably detect and recognise meter readings from the different meter kinds. For the task of digit recognition, a YOLOv5 based custom-built digit optical character reader is used that can recognise 0-to-9-digit numbers. Furthermore, the proposed AMR system achieves remarkable recognition rates of 99.74% for counters and 88.70% for digit recognition even while rejecting counters with lower confidence values.

关键词： Automated Detection Automatic Meter Reading Convolution Neural Network Deep Learning Image Segmentation Object Detection

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Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method

arXiv

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arXiv 2021年

作者： Guo, Theron Rokoš, Ondřej Veroy, Karen Centre for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Netherlands Mechanics of Materials Department of Mechanical Engineering Eindhoven University of Technology Eindhoven5612 AZ Netherlands

In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the microstructure is thus explicitly modeled inside the macrostructure, leading to a coupled two-scale formulation. Unfortunately, the high computational costs of such multiscale simulations often render the solution of design, optimization, or inverse problems infeasible. To address this issue, we propose in this work a non-intrusive reduced basis method to construct inexpensive surrogates for parametrized microscale problems;the method is specifically well-suited for multiscale simulations since the coupled simulation is decoupled into two independent problems: (1) solving the microscopic problem for different (loading or material) parameters and learning a surrogate model from the data;and (2) solving the macroscopic problem with the learned material model. The proposed method has three key features. First, the microscopic stress field can be fully recovered, which is useful for instance for revealing local stress concentrations inside the microstructure. Second, the method is able to accurately predict the stress field for a wide range of material parameters;furthermore, the derivatives of the effective stress with respect to the material parameters are available and can be readily utilized in solving optimization problems. Finally, it is more data efficient, i.e. requiring less training data, as compared to directly performing a regression on the effective stress. To construct the surrogate model, first, a proper orthogonal decomposition is performed on precomputed microscopic stress field snapshots to find a reduced basis for the stress. Second, a regression is employed to infer the coefficients of the reduced basis approximation for any arbitrary parameter value, thus enabling a rapid online evaluation of the microscopic stress.

关键词： Microstructure

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Four horizons for enhancing the performance of parallel simulations based on partial differential equations 6

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6th International European Conference on Parallel computing, Euro-Par 2000

作者： Keyes, David E. Department of Mathematics and Statistics Old Dominion University NorfolkVA23529-0077 United States Institute for Scientific Computing Research Lawrence Livermore National Laboratory LivermoreCA94551-9989 United States Institute for Computer Applications in Science and Engineering NASA Langley Research Center HamptonVA23681-2199 United States

ISBN: (纸本)9783540679561

Simulations of PDE-based systems, such as flight vehicles, the global climate, petroleum reservoirs, semiconductor devices, and nuclear weapons, typically perform an order of magnitude or more below other scientific simulations (e.g., from chemistry and physics) with dense linear algebra or N-body kernels at their core. In this presentation, we briefly review the algorithmic structure of typical PDE solvers that is responsible for this situation and consider possible architectural and algorithmic sources for performance improvement. Some of these improvements are also applicable to other types of simulations, but we examine their consequences for PDEs: potential to exploit orders of magnitude more processor-memory units, better organization of the simulation for today’s and likely near-future hierarchical memories, alternative formulations of the discrete systems to be solved, and new horizons in adaptivity. Each category is motivated by recent experiences in computational aerodynamics at the 1 Teraflop/s scale. © Springer-Verlag Berlin Heidelberg 2000.

关键词： Semiconductor devices

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Fine-grain parallelism using multi-core, Cell/BE, and GPU Systems

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PARALLEL computing 2012年第8期38卷 365-390页

作者： [Anonymous] [a] SiPS INESC-ID/IST Universidade Técnica de Lisboa Rua Alves Redol 9 1000-029 Lisbon Portugal [b] CASPER Department of Computer Science University of Cyprus P.O. Box 20537 CY 1678 Nicosia Cyprus [c] The Exelixis Lab Scientific Computing Group Heidelberg Institute for Theoretical Studies Scholss-Wolfsbrunnenweg 35 D-69118 Heidelberg Germany [d] National Center for Supercomputing Applications University of Illinois at Urbana-Champaign 1205 West Clark Street Urbana IL 61801 USA

Currently, we are facing a situation where applications exhibit increasing computational demands and where a large variety of parallel processor systems are available. In this paper we focus on exploiting fine-grain parallelism for three applications with distinct characteristics: a Bioinformatics application (MrBayes), a Molecular Dynamics application (NAMD), and a database application (TPC-H). We assess, side-by-side, the performance of the three applications on general-purpose multi-core processors, the Cell Broadband Engine (Cell/BE), and Graphics Processing Units (GPU). Our results indicate that application performance depends on the characteristics of the parallel architectures and on the computational requirements of the core functions of the respective applications. For MrBayes the best overall performance is achieved on general-purpose multi-core processors, for NAMD on the Cell/BE, and for TPC-H on GPUs. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Multi-core processors Multi-core acelerators Performance evaluation Fine-grain parallelism scientific workloads Database workloads

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Caffeine: Towards uniformed representation and acceleration for deep convolutional neural networks

Caffeine: Towards uniformed representation and acceleration ...

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IEEE International Conference on computer-Aided Design

作者： Chen Zhang Zhenman Fang Peipei Zhou Peichen Pan Jason Cong Center for Energy-Efficient Computing and Applications Peking University Beijing China Falcon-computing Inc. USA UCLA Computer Science Department University of California Los Angeles USA UCLA Peking University and the chief scientific advisor at Falcon Computing Solutions

ISBN: (纸本)9781509034215

With the recent advancement of multilayer convolutional neural networks (CNN), deep learning has achieved amazing success in many areas, especially in visual content understanding and classification. To improve the performance and energy-efficiency of the computation-demanding CNN, the FPGA-based acceleration emerges as one of the most attractive alternatives. In this paper we design and implement Caffeine, a hardware/software co-designed library to efficiently accelerate the entire CNN on FPGAs. First, we propose a uniformed convolutional matrix-multiplication representation for both computation-intensive convolutional layers and communication-intensive fully connected (FCN) layers. Second, we design Caffeine with the goal to maximize the underlying FPGA computing and bandwidth resource utilization, with a key focus on the bandwidth optimization by the memory access reorganization not studied in prior work. Moreover, we implement Caffeine in the portable high-level synthesis and provide various hardware/software definable parameters for user configurations. Finally, we also integrate Caffeine into the industry-standard software deep learning framework Caffe. We evaluate Caffeine and its integration with Caffe by implementing VGG16 and AlexNet network on multiple FPGA platforms. Caffeine achieves a peak performance of 365 GOPS on Xilinx KU060 FPGA and 636 GOPS on Virtex7 690t FPGA. This is the best published result to our best knowledge. We achieve more than 100× speedup on FCN layers over previous FPGA accelerators. An end-to-end evaluation with Caffe integration shows up to 7.3× and 43.5× performance and energy gains over Caffe on a 12-core Xeon server, and 1.5× better energy-efficiency over the GPU implementation on a medium-sized FPGA (KU060). Performance projections to a system with a high-end FPGA (Virtex7 690t) shows even higher gains.

关键词： Field programmable gate arrays Acceleration Bandwidth Machine learning Convolution Graphics processing units Kernel

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Fast collocation methods for high-dimensional weakly singular integral equations

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Journal of Integral Equations and applications 2008年第1期20卷 49-92页

作者： Chen, Zhongying Wu, Bin Xu, Yuesheng Department of Scientific Computing and Computer Applications Sun Yat-sen University Guangzhou 510275 China Department of Mathematics Syracuse University Syracuse NY 13244-1150 United States

We realize fast collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels on a polyhedral domain in Rd with d ≥ 3. A polyhedral domain is subdivided into a finite num...

We realize fast collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels on a polyhedral domain in R^d with d ≥ 3. A polyhedral domain is subdivided into a finite number of simplices. We construct a uniform self-similar partition of a simplex for the purpose of constructing multi-scale bases and their corresponding collocation functionals. The multi-scale bases and the collocation functionals lead to a compression of the matrix representation of the weakly singular integral operator and thus to a fast collocation scheme for solving the integral equation. We develop a quadrature rule for computing the weakly singular integrals appearing in the matrix. We propose an error control strategy for the numerical integration so that the nearly optimal convergence order for the discrete fast collocation method is obtained. Finally, a numerical experiment of solving the three-dimensional equation is presented to confirm the theoretical estimates. © 2008 Rocky Mountain Mathematics Consortium.

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Search-in-Memory (SiM): Reliable, Versatile, and Efficient Data Matching in SSD's NAND Flash Memory Chip for Data Indexing Acceleration

arXiv

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arXiv 2024年

作者： Chen, Yun-Chih Chang, Yuan-Hao Kuo, Tei-Wei The Department of Computer Science TU Dortmund Germany The Institute of Information Science Academia Sinica Taipei115 Taiwan Department of Computer Science and Information Engineering High Performance and Scientific Computing Center Center of Data Intelligence: Technologies Applications and Systems of National Taiwan University Taiwan

To index the increasing volume of data, modern data indexes are typically stored on SSDs and cached in DRAM. However, searching such an index has resulted in significant I/O traffic due to limited access locality and inefficient cache utilization. At the heart of index searching is the operation of filtering through vast data spans to isolate a small, relevant subset, which involves basic equality tests rather than the complex arithmetic provided by modern CPUs. We introduce the Search-in-Memory (SiM) chip, which demonstrates the feasibility of performing data filtering directly within a NAND flash memory chip, transmitting only relevant search results rather than complete pages. Instead of adding complex circuits, we propose repurposing existing circuitry for efficient and accurate bitwise parallel matching. We demonstrate how different data structures can use our flexible SIMD command interface to offload index searches. This strategy not only frees up the CPU for more computationally demanding tasks, but it also optimizes DRAM usage for write buffering, significantly lowering energy consumption associated with I/O transmission between the CPU and DRAM. Extensive testing across a wide range of workloads reveals up to a 9X speedup in write-heavy workloads and up to 45% energy savings due to reduced read and write I/O. Furthermore, we achieve significant reductions in median and tail read latencies of up to 89% and 85% respectively. Copyright © 2024, The Authors. All rights reserved.

关键词： Energy utilization

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A practical guide to machine learning interatomic potentials – Status and future

arXiv

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arXiv 2025年

作者： Jacobs, Ryan Morgan, Dane Attarian, Siamak Meng, Jun Shen, Chen Wu, Zhenghao Xie, Clare Yijia Yang, Julia H. Artrith, Nongnuch Blaiszik, Ben Ceder, Gerbrand Choudhary, Kamal Csanyi, Gabor Cubuk, Ekin Dogus Deng, Bowen Drautz, Ralf Fu, Xiang Godwin, Jonathan Honavar, Vasant Isayev, Olexandr Johansson, Anders Kozinsky, Boris Martiniani, Stefano Ong, Shyue Ping Poltavsky, Igor Schmidt, K.J. Takamoto, So Thompson, Aidan Westermayr, Julia Wood, Brandon M. Department of Materials Science and Engineering University of Wisconsin-Madison MadisonWI55705 United States Harvard University Center for the Environment Harvard University CambridgeMA02138 United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States Materials Chemistry and Catalysis Debye Institute for Nanomaterials Science Utrecht University Utrecht3584 CG Netherlands Globus University of Chicago ChicagoIL United States Data Science and Learning Division Argonne National Laboratory LemontIL United States Department of Materials Science and Engineering University of California BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Laboratory CA94720 United States Material Measurement Laboratory National Institute of Standards and Technology GaithersburgMD20899 United States Department of Engineering University of Cambridge CambridgeCB2 1PZ United Kingdom Google DeepMind Mountain ViewCA United States Ruhr-Universität Bochum Bochum44780 Germany Meta United States Orbital Materials London United Kingdom Department of Computer Science and Engineering The Pennsylvania State University University ParkPA United States College of Information Sciences and Technology The Pennsylvania State University University ParkPA United States Artificial Intelligence Research Laboratory The Pennsylvania State University University ParkPA United States Center for Artificial Intelligence Foundations and Scientific Applications The Pennsylvania State University University ParkPA United States Department of Chemistry Mellon College of Science Carnegie Mellon University PittsburghPA15213 United States Computational Biology Department School of Computer Science Carnegie Mellon University PittsburghPA15213 United States Courant Institute of Mathematical Sciences New York University New YorkNY10003 United States Center for Soft Matter Research Department of P

The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3-10+ years. © 2025, CC BY.

关键词： Digital storage

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The discrete multi-projection method for fredholm integral equations of the second kind

引用

Journal of Integral Equations and applications 2007年第2期19卷 143-162页

作者： Chen, Zhongying Long, Guangqing Nelakanti, Gnaneshwar Department of Scientific Computing and Computer Applications Sun Yat-Sen University Guangzhou 510275 China Department of Mathematics Guangxi Normal College Nanning 530001 China Department of Mathematics Indian Institute of Technology Kharagpur-721302 India

In this paper, discrete multi-projection methods are developed for solving the second kind Fredholm integral equations. We propose a theoretical framework for analysis of the convergence of these methods. The theory is then applied to establish super-convergence results for the corresponding discrete Galerkin method, collocation method and their iterated solutions. Numerical examples are presented to illustrate the theoretical estimates for the error of these methods. © 2007 Rocky Mountain Mathematics Consortium.

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