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SSRN 2024年

作者： Zhong, Mingliang Xiao, Tianbai Krause, Mathias J. Frank, Martin Simonis, Stephan Scientific Computing Center Karlsruhe Institute of Technology Eggenstein-Leopoldshafen76344 Germany State Key Laboratory of High Temperature Gas Dynamics Centre for Interdisciplinary Research in Fluids Institute of Mechanics Chinese Academy of Sciences Beijing100190 China School of Engineering Science University of Chinese Academy of Sciences Beijing100049 China Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76131 Germany Institute of Mechanical Process Engineering and Mechanics Karlsruhe Institute of Technology Karlsruhe76131 Germany Lattice Boltzmann Research Group Karlsruhe Institute of Technology Karlsruhe76131 Germany

Efficient modeling and simulation of uncertainties in computational fluid dynamics (CFD) remains a crucial challenge. In this paper, we present the first stochastic Galerkin (SG) lattice Boltzmann method (LBM) built upon the generalized polynomial chaos (gPC). The proposed method offers an efficient and accurate approach that depicts the propagation of uncertainties in stochastic incompressible flows. Formal analysis shows that the SG LBM preserves the correct Chapman-Enskog asymptotics and recovers the corresponding macroscopic fluid equations. Numerical experiments, including the Taylor-Green vortex flow, lid-driven cavity flow, and isentropic vortex convection, are presented to validate the solution algorithm. The results demonstrate that the SG LBM achieves the expected spectral convergence and the computational cost is significantly reduced compared to the sampling-based non-intrusive approaches, e.g., the routinely used Monte Carlo method. We obtain a speedup factor of 5.72 compared to Monte Carlo sampling in a randomized two-dimensional Taylor-Green vortex flow test case. By leveraging the accuracy and flexibility of LBM and the efficiency of gPC-based SG, the proposed SG LBM provides a powerful framework for uncertainty quantification in CFD practice. © 2024, The Authors. All rights reserved.

关键词： Computational fluid dynamics

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EXPLICIT RUNGE–KUTTA METHODS THAT ALLEVIATE ORDER REDUCTION

arXiv

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arXiv 2023年

作者： Biswas, Abhijit Ketcheson, David I. Roberts, Steven Seibold, Benjamin Shirokoff, David Computer Electrical and Mathematical Sciences & Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Department of Mathematical Sciences New Jersey Institute of Technology NewarkNJ07102 United States

Explicit Runge–Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high-order convergence for linear problems;we refer to these conditions as weak stage order conditions. We prove a general relationship between the method’s order, weak stage order, and number of stages. We derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear *** Codes 65L04, 65L20, 65M12 Copyright © 2023, The Authors. All rights reserved.

关键词： Runge Kutta methods

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Multi-Channel Hypergraph Convolution Group Recommendation with Member Information Enhancement

Multi-Channel Hypergraph Convolution Group Recommendation wi...

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IEEE International Conference on High Performance computing and Communications (HPCC)

作者： Tianhao Chen Qian Gao Jun Fan Key Laboratory of Computing Power Network and Information Security Ministry of Education Shandong Computer Science Center Qilu University of Technology (Shandong Academy of Sciences) Jinan Shandong China Shandong Engineering Research Center of Big Data Applied Technology Faculty of Computer Science and Technology Qilu University of Technology (Shandong Academy of Sciences) Jinan Shandong China Shandong Provincial Key Laboratory of Computer Networks Shandong Fundamental Research Center for Computer Science Jinan Shandong China China Telecom Digital Intelligence Techonology Co Ltd Jinan Shandong China

Group recommendation involves comprehensively considering various aspects, including members and items, to predict the overall interests of a group and recommend suitable items through a recommendation system. With the rapid evolution of the Internet, online group activities have become increasingly prevalent, making group recommendation a highly discussed topic within the realm of recommendation systems. However, current research in group recommendation still confronts the following challenges. Firstly, a predominant portion of group recommendation research focuses solely on aggregating group-level information, neglecting the valuable contribution of higher-order member-level insights to group recommendation. Moreover, some aggregation strategies overly prioritize fairness, thereby disregarding common real-world patterns. Secondly, previous studies have primarily relied on aggregating individual member interests to establish group preferences, lacking a holistic consideration of group dynamics. To tackle these challenges, this study introduces an innovative approach by implementing multi-channel hypergraph convolution within the member perspective. This approach aims to effectively extract higher-order insights from members by utilizing a member information enhancement module. By establishing group interconnections based on similarity and employing an adaptive fusion network to amalgamate multiple viewpoints, a final representation is derived. Experimental results demonstrate that our proposed model surpasses baseline models by 3% to 4% in terms of hit rate and accuracy, validating the efficacy of our approach.

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A Class of Smoothing-regularization Methods to Mathematical Programs with Vanishing Constraints

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数学进展 2024年第5期53卷 953-973页

作者： HU Qingjie MA Lili CHEN Yu School of Mathematics and Computing Science Guangci Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinGuangci541002P.R.China Center for Applied Mathematics of Guangri(GUET) GuilinGuangri541002P.R.China College of General Education Guangdong University of Science and TechnologyDongguanGuangdong523668P.R.China School of Mathematics and Statistics Guangri Normal UniversityGuilinGuangci541004P.R.China

this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing *** methods include the smoothing-regularization method proposed by Kanzow et ***[***.,2013,55(3):733-767]as a special *** the weaker conditions than the ones that have been used by Kanzow et *** 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization *** also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary ***,numerical experiments are given to show the efficiency of the proposed methods.

关键词： mathematical programs with vanishing constraints smoothing-regularization method VC-MFCQ strong stationary point

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MAP-based Problem-Agnostic Diffusion Model for Inverse Problems

arXiv

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arXiv 2025年

作者： Tao, Pingping Liu, Haixia Su, Jing Yang, Xiaochen Tan, Hongchen Shandong University Library No. 180 West Culture Road Shandong Weihai264209 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology No. 1037 Luoyu road Hubei Wuhan430074 China Dapartment of Basic Sciences Dalian University of Science and Technology No. 999-26 Harbor Road Liaoning Dalian116052 China School of Computer Science and Technology Harbin Institute of Technology No. 2 West Culture Road Shandong Weihai264209 China Institute of Future Technology Dalian University of Technology No. 2 Lingong Road Liaoning Dalian116081 China

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes’ rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods—for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting. Our numerical implementation is available at https://***/liuhaixias1/ MAP-DIFFUSION-IP. Copyright © 2025, The Authors. All rights reserved.

关键词： Inverse problems

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Global-aware beam search for neural abstractive summarization 21

Global-aware beam search for neural abstractive summarizatio...

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Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Ye Ma Zixun Lan Lu Zong Kaizhu Huang Department of Financial and Actuarial Mathematics School of Science and Laboratory for Intelligent Computing and Financial Technology Xi'an Jiaotong-Liverpool University SIP Suzhou China Department of Applied Mathematics School of Science and Laboratory for Intelligent Computing and Financial Technology Xi'an Jiaotong-Liverpool University SIP Suzhou China Department of Intelligent Science School of Advanced Technology

ISBN: (纸本)9781713845393

This study develops a calibrated beam-based algorithm with awareness of the global attention distribution for neural abstractive summarization, aiming to improve the local optimality problem of the original beam search in a rigorous way. Specifically, a novel global protocol is proposed based on the attention distribution to stipulate how a global optimal hypothesis should attend to the source. A global scoring mechanism is then developed to regulate beam search to generate summaries in a near-global optimal fashion. This novel design enjoys a distinctive property, i.e., the global attention distribution could be predicted before inference, enabling step-wise improvements on the beam search through the global scoring mechanism. Extensive experiments on nine datasets show that the global (attention)-aware inference significantly improves state-of-the-art summarization models even using empirical hyper-parameters. The algorithm is also proven robust as it remains to generate meaningful texts with corrupted attention distributions. The codes and a comprehensive set of examples are available.

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HOMOGENIZATION OF THE DISTRIBUTION-DEPENDENT STOCHASTIC ABSTRACT FLUID MODELS

arXiv

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arXiv 2023年

作者： Chen, Junlong Qiu, Zhaoyang Tang, Yanbin School of Sciences Great Bay University Great Bay Institute for Advanced Study Dongguan523000 China School of Mathematics University of Science and Technology of China Anhui Hefei230026 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210046 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the two−scale convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models which are the type of nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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A quantum-classical hybrid algorithm with Ising model for the learning with errors problem

arXiv

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arXiv 2024年

作者： Zheng, Muxi Zeng, Jinfeng Yang, Wentao Chang, Pei-Jie Yan, Bao Zhang, Haoran Wang, Min Wei, Shijie Long, Gui-Lu Beijing Academy of Quantum Information Sciences Beijing100193 China State Key Laboratory of Low-Dimensional Quantum Physics Department of Physics Tsinghua University Beijing100084 China State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou450001 China Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University Singapore Singapore Frontier Science Center for Quantum Information Beijing100084 China Beijing National Research Center for Information Science and Technology Beijing100084 China

The Learning-With-Errors (LWE) problem is a crucial computational challenge with significant implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model (HAWI) to address the LWE problem. Our approach involves transforming the LWE problem into the Shortest Vector Problem (SVP), using variable qubits to encode lattice vectors into an Ising Hamiltonian. We then identify the low-energy levels of the Hamiltonian to extract the solution, making it suitable for implementation on current noisy intermediate-scale quantum (NISQ) devices. We prove that the number of qubits required is less than m(3m -1)/2, where m is the number of samples in the algorithm. Our algorithm is heuristic, and its time complexity depends on the specific quantum algorithm employed to find the Hamiltonian's low-energy levels. If the Quantum Approximate Optimization Algorithm (QAOA) is used to solve the Ising Hamiltonian problem, and the number of iterations satisfies y © 2024, CC BY-NC-ND.

关键词： Qubits

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Exploring the unexpected: Disharmonized harmonic pulsation modes in high-amplitude δ Scuti stars

arXiv

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arXiv 2024年

作者： Xue, Hui-Fang Niu, Jia-Shu Department of Physics Taiyuan Normal University Jinzhong030619 China Institute of Computational and Applied Physics Taiyuan Normal University Jinzhong030619 China Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology Jinzhong030619 China Institute of Theoretical Physics Shanxi University Taiyuan030006 China State Key Laboratory of Quantum Optics and Quantum Optics Devices Shanxi University Taiyuan030006 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi030006 China

Harmonics are a ubiquitous feature across various pulsating stars. They are traditionally viewed as mere replicas of the independent primary pulsation modes and have thus been excluded from asteroseismological models. Recent research, however, has uncovered a significant discrepancy: in high-amplitude δ Scuti (HADS) stars, harmonics exhibit uncorrelated variations in amplitude and frequency relative to their independent primary pulsation modes. The nature of these disharmonized harmonics is a question of critical importance. In our study we analysed five triple-mode HADS stars observed by the Transiting Exoplanet Survey Satellite (TESS) and discovered some pervasive patterns of disharmonized harmonics in both the fundamental ( f0) and first overtone ( f1) pulsation modes. Intriguingly, through an in-depth frequency interaction analysis of V1393 Cen, we identified 2 f1as an independent pulsation mode, distinct from f1, and identified it as the progenitor of the frequency variations observed in 3 f1, 4 f1, 5 f1, and 6 f1. Similar behaviour can be found in DO CMi and GSC 06047-00749, in which 2 f1and 3 f1are the independent pulsation modes, respectively. Notably, we found an interesting pattern when decomposing the harmonics that might suggest a generation process of harmonics. These findings serve as a new window on the research of harmonics, which remains a hidden corner of contemporary asteroseismology. © 2024, CC BY.

关键词： Stars

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Quantum Entanglement Based on Two-Photon Joint Subtraction from Two-Mode Squeezed Vacuum States

Quantum Entanglement Based on Two-Photon Joint Subtraction f...

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OptoElectronics and Communications Conference, OECC

作者： Hongbin Song Heyu Huang Hao Liu Ai Zhou Guofeng Zhang Hidehiro Yonezawa The General Education Division and Guangdong Key Laboratory of Optoelectronic Materials and Chips and Shenzhen Key Lab of Semiconductor Lasers The Chinese University of Hong Kong Shenzhen Shenzhen China School of Materials Science and Engineering and National Engineering Research Center of Fiber Optic Sensing Technology and Networks Wuhan University of Technology Wuhan China National Engineering Research Center of Fiber Optic Sensing Technology and Networks Wuhan University of Technology Wuhan China Department of Applied Mathematics The Hong Kong Polytechnic University Hongkong China Optical Quantum Control Research Team RIKEN Center for Quantum Computing Saitama Japan

We present and analyze the quantum entanglement generated from two-photon joint subtraction from two-mode squeezed vacuum states (TMSV). Larger entanglement negativity than single-photon jointly subtracted TMSV, photo... 详细信息

ISBN: (数字)9798350308396

ISBN: (纸本)9798350308402

关键词： Protocols Correlation Quantum entanglement Simulation Elementary particle vacuum Quantum networks Photonics

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