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arXiv 2023年

作者： Alappat, Christie Thies, Jonas Hager, Georg Fehske, Holger Wellein, Gerhard Erlangen National High Performance Computing Center Friedrich-Alexander-Universität Erlangen-Nürnberg Germany Institute of Applied Mathematics Delft University of Technology Delft Netherlands Department of Computer Science Friedrich-Alexander-Universität Erlangen-Nürnberg Germany

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety of approaches has been proposed to make these polynomial evaluations explicit (i.e., fix the coefficients), e.g., polynomial preconditioners or s-step Krylov methods. Furthermore, it is nowadays a popular practice to approximate triangular solves by a matrix polynomial to increase parallelism. Such algorithms allow to evaluate the polynomial using a so-called matrix power kernel (MPK), which computes the product between a power of a sparse matrix A and a dense vector x, i.e., Apx, or a related operation. Recently we have shown that using the level-based formulation of sparse matrix-vector multiplications in the Recursive Algebraic Coloring Engine (RACE) framework we can perform temporal cache blocking of MPK to increase its performance. In this work, we demonstrate the application of this cache-blocking optimization in sparse iterative solvers. By integrating the RACE library into the Trilinos framework, we demonstrate the speedups achieved in (preconditioned) s-step GMRES, polynomial preconditioners, and algebraic multigrid (AMG). For MPK-dominated algorithms we achieve speedups of up to 3× on modern multi-core compute nodes. For algorithms with moderate contributions from subspace orthogonalization, the gain reduces significantly, which is often caused by the insufficient quality of the orthogonalization routines. Finally, we showcase the application of RACE-accelerated solvers in a real-world wind turbine simulation (Nalu-Wind) and highlight the new opportunities and perspectives opened up by RACE as a cache-blocking technique for MPK-enabled sparse solvers. Copyright © 2023, The Authors. All rights reserved.

关键词： Polynomials

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Application of Lasso regression model in the analysis of success probability of electronic experiments

Application of Lasso regression model in the analysis of suc...

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2021 IEEE International Conference on Computer Science, Electronic Information Engineering and Intelligent Control Technology, CEI 2021

作者： Wei, Haomin Wang, Ruihua Guo, Zhangxia Yang, Zhou Wang, Jiajia College of Mechatronic Engineering North University of China Taiyuan China PLA Academy of Military Science China Innovation Center for Intelligent System on Recognition and Decision China Aerospace Science and Industry Corporation Applied Mathematics Research Center Beijing Jinghang Research Institute of Computing and Communication Beijing China

ISBN: (纸本)9780738146492

The multifactorial electronic experiment design and evaluation process suffer from many test constraints, complex and diverse test factors, and multiple indicators coupled with each other. In the face of these problems, this paper firstly elaborates the role relationship between different multifactorial electronic experiment states and influencing factors, and the basic explanation of parametric modeling and regression analysis. The logic of the Lasso regression model are elaborated, and the parametric modeling method is used to evaluate and model the factors and their relationships that affect the success probability of a trial in one case with multiple regression models, and the results are analyzed and evaluated horizontally. The results prove that the Lasso regression method is more controllable and the results are more interpretable by adjusting the parameters, and the maximum error is reduced, which has better applicability;the Least Squares method and the Logistic method also have their excellent characteristics, and in practical applications, suitable regression algorithms can be selected for use according to the requirements of the scenario. © 2021 IEEE.

关键词： Regression analysis

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Data-driven approach for generating colormaps of scientific simulation data 14

Data-driven approach for generating colormaps of scientific ...

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14th IADIS International Conference Computer Graphics, Visualization, Computer Vision and Image Processing 2020, CGVCVIP 2020 and 5th IADIS International Conference Big Data Analytics, Data Mining and Computational Intelligence 2020, BigDaCI 2020 and 9th IADIS International Conference Theory and Practice in Modern computing 2020, TPMC 2020, Part of the 14th Multi Conference on Computer Science and Information Systems, MCCSIS 2020

作者： Cao, Yi Wang, Xiaohua Wang, Huawei Ai, Zhiwei Xia, Fang High Performance Computing Center Institute of Applied Physics and Computational Mathematics Beijing China CAEP Software Center for High Performance Numerical Simulation Beijing China

ISBN: (纸本)9789898704214

The colormap plays important roles in the exploration, analysis, and discovery of scientific data. Datasets generated by real-world simulation applications are becoming increasingly more complex: the distribution of the variable values within the data is often extremely uneven and accompanied by high levels of data noise. The heterogeneity of these data characteristics presents rich information about physical laws as well as technical challenges for colormap of visualization. Most default colormaps are defined by linearly interpolating dataset values and cannot be adapted to convey the physical meaning behind complicated data. In this paper, we introduce a data-driven approach for generating colormaps of scientific simulation data, that can overcome the visualization problems using noise-reduction-based parameter tuning of color control points and a wave-like colormap enhancement in brightness. Several real-world simulation data are used to verify the effectiveness of our proposed method, which means that our method could help domain scientists understand complicated data more clearly and quickly. © Proceedings of the 14th IADIS International Conference Computer Graphics, Visualization, Computer Vision and Image Processing 2020, CGVCVIP 2020 and Proceedings of the 5th IADIS International Conference Big Data Analytics, Data Mining and Computational Intelligence 2020, BigDaCI 2020 and Proceedings of the 9th IADIS International Conference Theory and Practice in Modern computing 2020, TPMC 2020 - Part of the 14th Multi Conference on Computer Science and Information Systems, MCCSIS 2020. All rights reserved.

关键词： Data visualization

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Unification of integral transforms and their applications

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Partial Differential Equations in applied mathematics 2024年 10卷

作者： Belafhal, A. El Aitouni, R. Usman, T. LPNAMME Laser Physics Group Department of Physics Faculty of Sciences Chouaïb Doukkali University P. B 20 El Jadida 24000 Morocco Preparatory Studies Center Mathematics and Computing Skills Unit University of Technology and Applied Sciences Sur 411 Oman

An integral transform called BA-transform is introduced in this work, which yields a known number of transforms by changing variables. We prove that Laplace, Sumudu, Natural, Elzaki, Aboodh, Tarig, Srivastava, Kamal, Laplace–Carson, Mohand, Shehu and Sawi transforms are the particular cases of our new generalized integral transform. We establish for our transform few fundamental properties, connections with these well-known integral transforms in literature and some test examples with their graphic illustrations in application section. Also, the double new integral transform and some of its fundamental properties are investigated. Some results and relationships between our simple and double integral transforms are also established. © 2024 The Author(s)

关键词： B-transform BA-transform BB-transform Differential equations Partial differential equations

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Immersive Embedded Consumer Model Leveraging AI with Zero-Trust Architecture for Cyber-Physical System

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IEEE Transactions on Consumer Electronics 2025年

作者： Rehman, Amjad Haseeb, Khalid Kolivand, Hoshang Saba, Tanzila Al-Khasawneh, Mahmoud A. Ahmad, Shabir Ullah, Inam Lab Riyadh12435 Saudi Arabia Liverpool John Moores University School of Computer Science and Mathematics United Kingdom School of Computing and Digital Technologies Staffordshire University Liverpool Staffordshire United Kingdom University City Sharjah 1797 United Arab Emirates Hourani Center for Applied Scientific Research Al-Ahliyya Amman University Jordan School of Computing Skyline University College Sharjah United Arab Emirates Incheon Startup Park Center of Artificial Intelligence for Medical Instruments Convensia-daero Incheon204 Korea Republic of Gachon University Department of Computer Engineering Seongnam13120 Korea Republic of

The rapid expansion of the wireless network and its combination with the Consumer Internet of Things (CIoT) has introduced significant research challenges for Cyber-Physical Systems (CPS). The distributed nature of these embedded networks provides big data analytics with the integration of sensors, electronic devices, hardware, and network components. They provide diverse functionalities while sensing the observing environment based on the demand of network users with timely feedback, which supports efficient decision-making. However, CIoT devices in CPS increasingly interact with both physical and digital environments, such interaction raises the research challenges of performance optimization, data breaches, and long-run seamless connectivity. In addition, the constraint devices demanded lightweight communication methods to remain robust and enhance network stability. This paper presents an adaptive model that leverages AI-based optimization techniques with efficient data management and utilization of resources in consumer applications. Moreover, the integrated edges provide consistency and resilience of communication services in unpredictable systems, while adopting a Zero-Trust architecture with more trustworthy and secure transmissions. It increases the system's scalability and improves the response time with the limited computing power of devices for real-time processing. Simulation results demonstrated the significant outcomes of the proposed model over the dynamic scenarios for packet delivery ratio by 35.5%, network throughput by 38.7%, energy consumption by 41.6%, and latency by 45% against existing solutions. © 1975-2011 IEEE.

关键词： consumer technologies edge intelligence embedded systems information security technological development

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GBFRS: Robust Fuzzy Rough Sets via Granular-ball computing

arXiv

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arXiv 2025年

作者： Xia, Shuyin Lian, Xiaoyu Sang, Binbin Wang, Guoyin Gao, Xinbo Chongqing Key Laboratory of Computational Intelligence Key Laboratory of Big Data Intelligent Computing Key Laboratory of Cyberspace Big Data Intelligent Security Ministry of Education Chongqing University of Posts and Telecommunications Chongqing400065 China College of Computer and Information Science the National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China

Fuzzy rough set theory is effective for processing datasets with complex attributes, supported by a solid mathematical foundation and closely linked to kernel methods in machine learning. Attribute reduction algorithms and classifiers based on fuzzy rough set theory exhibit promising performance in the analysis of high-dimensional multivariate complex data. However, most existing models operate at the finest granularity, rendering them inefficient and sensitive to noise, especially for high-dimensional big data. Thus, enhancing the robustness of fuzzy rough set models is crucial for effective feature selection. Muiti-garanularty granular-ball computing, a recent development, uses granular-balls of different sizes to adaptively represent and cover the sample space, performing learning based on these granular-balls. This paper proposes integrating multi-granularity granular-ball computing into fuzzy rough set theory, using granular-balls to replace sample points. The coarse-grained characteristics of granular-balls make the model more robust. Additionally, we propose a new method for generating granular-balls, scalable to the entire supervised method based on granular-ball computing. A forward search algorithm is used to select feature sequences by defining the correlation between features and categories through dependence functions. Experiments demonstrate the proposed model’s effectiveness and superiority over baseline methods. The source codes and datasets are both available on the public link: https://***/lianxiaoyu724/GBFRS Copyright © 2025, The Authors. All rights reserved.

关键词： Granular computing

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Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost

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Physical Review Letters 2023年第15期131卷 150603-150603页

作者： Dong An Jin-Peng Liu Lin Lin Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Mathematics University of California Berkeley California 94720 USA Simons Institute for the Theory of Computing University of California Berkeley California 94720 USA Center for Theoretical Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Lawrence Berkeley National Laboratory Applied Mathematics and Computational Research Division Berkeley California 94720 USA Challenge Institute for Quantum Computation University of California Berkeley California 94720 USA

We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

关键词： Open quantum systems Quantum algorithms Quantum algorithms & computation Quantum simulation Differential equations

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Reconstructing superoscillations buried deeply in noise

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Physical Review A 2024年第6期110卷 L061502-L061502页

作者： Derek D. White Shunxing Zhang Barbara Šoda Achim Kempf Daniele C. Struppa Andrew N. Jordan John C. Howell Institute for Quantum Studies Chapman University Orange California 92866 USA Perimeter Institute for Theoretical Physics Waterloo Ontario Canada N2L 2Y5 Department of Applied Mathematics University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Physics University of Waterloo Waterloo Ontario Canada N2L 3G1 Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 The Donald Bren Presidential Chair in Mathematics Chapman University Orange California 92866 USA The Kennedy Chair in Physics Chapman University Orange California 92866 USA Center for Coherence and Quantum Optics University of Rochester Rochester New York 14627 USA Department of Physics and Astronomy University of Rochester Rochester New York 14627 USA Racah Institute of Physics The Hebrew University of Jerusalem Jerusalem 91904 Israel

We utilize a method using frequency combs to construct waves that feature superoscillations—local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function—even ones well outside the bandlimits—to an arbitrary degree of accuracy. We experimentally demonstrate that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. We additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit.

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An alternated inertial general splitting method with linearization for the split feasibility problem

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Optimization 2023年第10期72卷 2585-2607页

作者： Qiao-Li Dong Lulu Liu Xiaolong Qin Jen-Chih Yao a Tianjin Key Laboratory for Advanced Signal Processing and College of Science Civil Aviation University of China Tianjin People's Republic of China b Department of Mathematics Hangzhou Normal University Hangzhou People's Republic of China c Research Center for Interneural Computing China Medical University Hospital China Medical University Taichung Taiwand Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan

In this paper, we propose an alternated inertial general splitting method with linearization for a split feasibility problem. Four rules of inertial parameters and relaxation parameters are discussed, where the adaptive inertial parameters are firstly investigated. The convergence of the proposed method is established under standard conditions. The numerical examples are presented to test four choices of the parameters and illustrate the advantage of our methods. An application in signal processing is presented to illustrate the recovery of the proposed algorithm for the sparse signal.

关键词： Split feasibility problem alternated inertial general splitting method with linearization general splitting methods with linearization alternated inertial CQ algorithm 47H05 47J20 47J25 65K15 90C25

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Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

arXiv

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arXiv 2023年

作者： Shen, Yizhi Camps, Daan Szasz, Aaron Darbha, Siva Klymko, Katherine Williams–Young, David B. Tubman, Norm M. Van Beeumen, Roel Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States NASA Ames Research Center Moffett FieldCA94035 United States

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition

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