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6th International Conference on Power and Energy Technology, ICPET 2024

作者： Su, Zhao-Gang Chen, Sheng-Jie Li, Yu-Fei Chen, Liang Kou, Caixia Cai, Zhi Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Beijing Key Laboratory of Research and System Evaluation of Power Dispatching Automation Technology China Electric Power Research Institute Beijing China

ISBN: (纸本)9798350375855

The unit commitment (UC) problem has been extensively researched in the literature, which is typically formulated as a mixed integer programming (MIP) problem. However, current studies lack effective methods to identify potential UC problem structures within a general MIP problem, making it challenging to leverage well-established valid inequalities for UC problems to accelerate the solution process. In this paper, we present a novel detection method that automatically identifies UC structures within an MIP problem by analyzing the relationships between variables and constraints. Moreover, we enhance the MIP formulation by incorporating three well-studied classes of valid inequalities as cutting planes, based on the identified UC structures. Our experiments demonstrate that our proposed UC detection method greatly improves computational efficacy of a standard MIP solver compared to the default setting. © 2024 IEEE.

关键词： Mixed-integer linear programming

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A Scalable Interior-Point Gauss-Newton Method for PDE-Constrained Optimization with Bound Constraints

arXiv

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arXiv 2024年

作者： Hartland, Tucker Petra, Cosmin G. Petra, Noémi Wang, Jingyi Center for Applied Scientific Computing Lawrence Livermore National Laboratory CA United States Department of Applied Mathematics University of California MercedCA United States

We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton optimization method. To cope with the poorly-conditioned IP-Gauss-Newton saddle-point linear systems that need to be solved, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE-constrained optimization problems. A block Gauss-Seidel preconditioner is proposed for the GMRES-based solution of the IP-Gauss-Newton linear systems. It is shown, for a large-class of PDE- and bound-constrained optimization problems, that the spectrum of the block Gauss-Seidel preconditioned IP-Gauss-Newton matrix is asymptotically independent of discretization and is not impacted by the ill-conditioning that notoriously plagues interior-point methods. We exploit symmetry of the IP-Gauss-Newton linear systems and propose a regularization and log-barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)based solution of the related IP-Gauss-Newton-Schur complement linear systems. The eigenvalues of the block Gauss-Seidel preconditioned IP-Gauss-Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log-barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on an example problem with bound and nonlinear elliptic PDE constraints. The numerical solution of the optimization problem is shown to require a discretization independent number of IP-Gauss-Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill-conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of preconditioner and linear system matrix applies, achieved with algebraic multigrid based solvers, and

关键词： Constrained optimization

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Fabric4show: real-time vision system for fabric defect detection and post-processing

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Visual Intelligence 2024年第1期2卷 1-13页

作者： Lin, Huaizhou Cai, Dan Xu, Zengmin Wu, Jinsong Sun, Lixian Jia, Haibin School of Materials Science and Engineering Guangxi Key Laboratory of Information Guilin University of Electronic Technology Guilin China School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Center for Applied Mathematics of Guangxi (GUET) Guilin China Anview.ai Guilin China School of Artificial Intelligence Guilin University of Electronic Technology Guilin China Department of Electrical Engineering University of Chile Santiago Chile

The exploration of computer vision applications for fabric defect detection has immense potential value. However, current relevant research in this area has primarily focused on detection models that aim for high detection accuracy and algorithmic efficiency, while neglecting the practical industrial production requirements. Therefore, we propose a fabric defect detection and post-processing system that integrates an optimized region with convolutional neural network (CNN) features (i.e., Faster R-CNN) for defect detection, defect localization and detection model evaluation. In addition, the proposed intelligent system incorporates novel approaches, such as a rearranged fabric dataset, anomaly detection, recommended clipping region division, and a replenishment device. This study illustrates an example of artificial intelligence (AI)-driven automated technology in fabric manufacturing. The accuracy and detection speed of different detection models under identical hardware conditions are evaluated and compared with related work. Experimental results demonstrate that the proposed approach achieves comparable performance to other models, while significantly reducing computational resource requirements. The potential efficiency of using two-stage networks on hardware systems for fabric defect detection tasks is highlighted, which is likely to have relevant implications for the textile industry. © The Author(s) 2024.

关键词： Automation Computer vision Defect detection Fabric manufacturing Faster R-CNN

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On the Existence and Uniqueness of Solutions to Delay Partial Differential Equations with Uncertainty 7

On the Existence and Uniqueness of Solutions to Delay Partia...

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7th International Conference on Optimization and Applications, ICOA 2021

作者： Amma, Bouchra Ben Melliani, Said Chadli, Lalla Saadia Sultan Moulay Slimane University Laboratory of Applied Mathematics and Scientific Computing Beni Mellal Morocco

ISBN: (纸本)9781665441032

Intuitionistic fuzzy partial differential equations with delay, one type of uncertain differential equations, are a very important field of study in theoretical and applications researches. Our aim in this paper is to establish suitable conditions for the existence and uniqueness of intuitionistic fuzzy solutions for delay partial differential equations with local initial conditions on a new weighted metric space. Our results are based on the properties of Banach fixed-point theorem. © 2021 IEEE.

关键词： Partial differential equations

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A Unified Norm Error Analysis of SAV-BDF Schemes for the Incompressible Navier–Stokes Equations

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Journal of Scientific computing 2024年第1期100卷 1-25页

作者： Ji, Bingquan Liao, Hong-lin Institute of Applied Physics and Computational Mathematics Beijing China School of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA) MIIT Nanjing China

This article is concerned with the $$L^2$$ norm error analysis of high-order BDF methods for the incompressible Navier–Stokes equation subjected to no-slip boundary conditions. To mitigate the complexity of high-order time-stepping algorithms caused by decoupling strategies, we combine the prediction–correction technique with a generalized scalar auxiliary variable approach to devise a family of linear, energy stable BDF schemes up to fifth-order accuracy in time. All the proposed schemes can be decoupled into a sequence of Poisson-type equations for the pressure and velocity fields, which significantly reduces the size of the linear systems at each time step. To deal with the essential difficulty raised by the non-A-stability of high-order BDF schemes, we introduce a class of discrete orthogonal convolution kernels to develop a unified framework for the $$L^2$$ norm convergence analysis of the proposed high-order BDF schemes. The velocity attains optimal rate of convergence in the $$L^2$$ norm under some mild mesh restrictions. Furthermore, building on the recent results concerning the positive definiteness of high-order BDF convolution kernels, we also provide an error estimate of the pressure in a weak $$L^2$$ norm. Benchmark examples including the Taylor–Green vortex problem and the regularized lid-driven cavity flow with Reynolds numbers up to 5000 are included to verify the stability and high accuracy of our numerical schemes.

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A New Polynomial Reconstruction Scheme Aeno-C for Ader Methods to Very-High Orders of Accuracy

SSRN

引用

SSRN 2025年

作者： Yajaman, Siddharth Toro, Eleuterio F. Dematte, Riccardo Laboratory for Scientific Computing University of Cambridge Cambridge United Kingdom Laboratory of Applied Mathematics University of Trento Trento Italy University of Toronto Institute for Aerospace Studies Toronto Canada

In this paper, we introduce AENO-C, a high-order polynomial reconstruction scheme that builds upon AENO by employing a special averaging of the ENO polynomial and a conservative polynomial from the centered stencil closest to the ENO stencil, using a new joining function with improved asymptotic properties. The scheme is systematically evaluated within the ADER finite volume framework up to tenth-order accuracy on test cases involving the linear advection equation, Burgers’ equation with a source term, and the Euler equations. It is found to perform highly satisfactorily across different scenarios, including both smooth and discontinuous profiles, and for all considered orders of accuracy. For smooth solutions, it exhibits convergence rates clearly superior to ENO and the original AENO, making it competitive and, in many situations, even more efficient than WENO in achieving a given error tolerance. For discontinuous solutions, it demonstrates remarkable robustness, effectively resolving complex features with high fidelity while preventing the appearance of spurious oscillations. The new reconstruction scheme is simple to implement, computationally cheap, comparable to ENO and AENO, and provides a closed form polynomial expression which can be evaluated at any desired point. © 2025, The Authors. All rights reserved.

关键词： Euler equations

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Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

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Communications in Computational Physics 2022年第8期32卷 829-849页

作者： Xiaoqiang Yue Jianmeng He Xiaowen Xu Shi Shu Libo Wang National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105P.R.China Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100094P.R.China College of Information Science and Technology JinanUniversityGuangzhou 510632P.R.China

We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high *** this article,motivated by[***,***,***,SIAM *** ***.33(2012)653–680]and[***,***,***,***.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear ***,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

关键词： Radiation diffusion equations Schwarz methods algebraic multigrid parallel and distributed computing

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Learning consensus and complementary bipartite graph through orthogonal transformation for multi-view subspace clustering

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Expert Systems with Applications 2025年 286卷

作者： Li, Xiangli Wei, Jiafeng Xie, Tengchi School of Mathematics and Computing Science Guilin University of Electronic Technology Guangxi 541004 China Center for Applied Mathematics of Guangxi Guangxi 541004 China Guangxi Colleges and University Key Laboratory of Data Analysis and Computation Guangxi 541004 China

In order to effectively utilize the consensus and complementary information in multi-view data to achieve better clustering performance, a large number of multi-view clustering algorithms have been proposed. A common multi-view subspace clustering method for mining consensus information is to learn a uniform consensus representation matrix for multiple views. But there are currently studies questioning the rationality of this method. To address this issue, the research in this paper establishes a link between view-specific representation matrices and consensus representation matrices, making the learning of consensus representation matrices more reasonable. Specifically, this paper considers the vectors formed by the representation coefficients of the samples as embeddings of the sample features in the Rm linear space, after which a mapping relationship will be established between the view-specific representation matrices and the consensus representation matrices to learn reasonable consensus representation matrices. Extensive experiments on eight benchmark datasets show that the proposed algorithm is effective and competitive. © 2025 Elsevier Ltd

关键词： Clustering algorithms

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Regularity for Diffusion Equations with Non-smooth Data

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Results in mathematics 2023年第4期78卷 1-22页

作者： Dondl, Patrick Zeinhofer, Marius Department of Applied Mathematics University of Freiburg Freiburg im Breisgau Germany Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

We prove an $$L^p(I,C^\alpha (\Omega ))$$ regularity result for a diffusion equation with mixed boundary conditions, $$L^\infty $$ coefficients and an $$L^{ q }$$ initial condition. We provide explicit control of the $$L^p(I,C^\alpha (\Omega ))$$ norm with respect to the data. To prove our result, we first establish $$C^\alpha (\Omega )$$ control of the stationary equation, extending a result by Haller-Dintelmann et al. (Appl Math Optim 60(3):397–428, 2009).

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computing the many-body Green's function with adaptive variational quantum dynamics

arXiv

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arXiv 2023年

作者： Gomes, Niladri Williams-Young, David B. de Jong, Wibe A. Applied Mathematics and Computing Sciences Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

We present a method to compute the many-body real time Green’s function using an adaptive variational quantum dynamics simulation approach. The real-time Green’s function involves time evolution of a quantum state with one additional electron with respect to the ground state wavefunction that is first expressed as a linear linear combination of state vectors. The real time evolution and the Green’s function is obtained by combining the dynamics of the individual statevectors in the linear combination. The use of the adaptive protocol enables us to generate compact ansätze on-the-fly while running the simulation. In order to improve the convergence of spectral features Padé approximants are applied to obtain the Fourier transform of the Green’s function. We demonstrate the evaluation of the Green’s function on a IBM Q quantum computer. As a part of our error mitigation strategy, we develop a resolution enhancing method that we successfully apply on the noisy data from the real quantum hardware. Copyright © 2023, The Authors. All rights reserved.

关键词： Quantum computers

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