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Multitask kernel-learning parameter prediction method for solving time-dependent linear systems

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arXiv 2022年

作者： Jiang, Kai Zhang, Juan Zhou, Qi Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well developed. In this paper, we present a multitask kernel-learning parameter prediction method to automatically obtain relatively optimal splitting parameters, which contains simultaneous multiple parameters prediction and a data-driven kernel learning. For solving time-dependent linear systems, including linear differential systems and linear matrix systems, we give a new matrix splitting Kronecker product method, as well as its convergence analysis and preconditioning strategy. Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. Moreover, our iteration method as a preconditioner can effectively accelerate GMRES. As the dimension of systems increases, all the advantages of our approaches becomes significantly. Especially, for solving the differential Sylvester matrix equation, the speedup ratio can reach tens to hundreds of times when the scale of the system is larger than one hundred thousand. Copyright © 2022, The Authors. All rights reserved.

关键词： Linear systems

A general alternating-direction implicit Newton method for solving complex continuous-time algebraic Riccati matrix equation

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arXiv 2022年

作者： Li, Shifeng Jiang, Kai Zhang, Juan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, applying the Newton method, we transform the complex continuous-time algebraic Riccati matrix equation into a Lyapunov equation. Then, we introduce an efficient general alternating-direction implicit (GADI) method to solve the Lyapunov equation. The inexact Newton-GADI method is presented to save computational amount effectively. Moreover, we analyze the convergence of the Newton-GADI method. The convergence rate of the Newton-GADI and Newton-ADI methods is compared by analyzing their spectral radii. Furthermore, we give a way to select the quasi-optimal parameter. Corresponding numerical tests are shown to illustrate the effectiveness of the proposed algorithms. © 2022, CC BY-SA.

关键词： Newton-Raphson method

ANISOTROPIC ANALYSIS OF VEM FOR TIME-HARMONIC MAXWELL EQUATIONS IN INHOMOGENEOUS MEDIA WITH LOW REGULARITY

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arXiv 2023年

作者： Chen, Chunyu Guo, Ruchi Wei, Huayi School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China Department of Mathematics University of California IrvineCA92697 United States

It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal convergence for low-regularity solutions heavily relies on conforming spaces and highly-regular simplicial meshes. This can be a significant limitation for many popular methods based on polytopal meshes in the case of inhomogeneous media, as the discontinuity of electromagnetic parameters can lead to quite low regularity of solutions near media interfaces, and potentially worsened by geometric singularities, making many popular methods based on broken spaces, non-conforming or polytopal meshes particularly challenging to apply. In this article, we present a virtual element method for solving an indefinite time-harmonic Maxwell equation in 2D inhomogeneous media with quite arbitrary polytopal meshes, and the media interface is allowed to have geometric singularity to cause low regularity. There are two key novelties: (i) the proposed method is theoretically guaranteed to achieve robust optimal convergence for solutions with merely Hθ regularity, θ ∈ (1/2, 1];(ii) the polytopal element shape can be highly anisotropic and shrinking, and an explicit formula is established to describe the relationship between the shape regularity and solution regularity. Extensive numerical experiments will be given to demonstrate the effectiveness of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Maxwell equations

A MULTI-CATEGORY INVERSE DESIGN NEURAL NETWORK AND ITS APPLICATION TO DIBLOCK COPOLYMERS

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arXiv 2022年

作者： Wei, Dan Zhou, Tiejun Huang, Yunqing Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this work, we design a multi-category inverse design neural network to map ordered periodic structure to physical parameters. The neural network model consists of two parts, a classifier and Structure-Parameter-Mapping (SPM) subnets. The classifier is used to identify structure, and the SPM subnets are used to predict physical parameters for desired structures. We also present an extensible reciprocal-space data augmentation method to guarantee the rotation and translation invariant of periodic structures. We apply the proposed network model and data augmentation method to two-dimensional diblock copolymers based on the Landau-Brazovskii model. Results show that the multi-category inverse design neural network is high accuracy in predicting physical parameters for desired structures. Moreover, the idea of multi-categorization can also be extended to other inverse design *** Codes 68T07, 35R30, 35Q68, 74E15, 03C64 Copyright © 2022, The Authors. All rights reserved.

关键词： Block copolymers

FOURIER NEURAL SOLVER FOR LARGE SPARSE LINEAR ALGEBRAIC SYSTEMS

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arXiv 2022年

作者： Cui, Chen Jiang, Kai Liu, Yun Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the Fourier Neural Solver (FNS), to address them. FNS is based on deep learning and Fast Fourier transform. Because the error between the iterative solution and the ground truth involves a wide range of frequency modes, FNS combines a stationary iterative method and frequency space correction to eliminate different components of the error. Local Fourier analysis reveals that the FNS can pick up on the error components in frequency space that are challenging to eliminate with stationary methods. Numerical experiments on the anisotropy diffusion equation, convection-diffusion equation, and Helmholtz equation show that FNS is more efficient and more robust than the state-of-the-art neural *** Codes 65F10 65N22 68T07 35Q68 Copyright © 2022, The Authors. All rights reserved.

关键词： Fourier analysis

γ-DEEPDSM FOR INTERFACE RECONSTRUCTION: OPERATOR LEARNING AND A LEARNING-AUTOMATED FEM PACKAGE

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arXiv 2024年

作者： Zheng, Yangyang Wei, Huayi Cao, Shuhao Guo, Ruchi School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China School of Science and Engineering University of Missouri-Kansas City Kansas CityMO United States School of Mathematics Sichuan University Sichuan Chengdu China

In this work, we propose an Operator Learning (OpL) method for solving boundary value inverse problems in partial differential equations (PDEs), focusing on recovering diffusion coefficients from boundary data. Inspired by the classical Direct Sampling Method (DSM), our operator learner, named γ-deepDSM, has two key components: (1) a data-feature generation process that applies a learnable fractional Laplace-Beltrami operator to the boundary data, and (2) a convolutional neural network that operates on these data features to produce reconstructions. To facilitate this workflow, leveraging FEALPy [52], a cross-platform Computed-Aided-engineering engine, our another contribution is to develop a set of finite element method (FEM) modules fully integrated with PyTorch, called Learning-Automated FEM (LA-FEM). The new LA-FEM modules in FEALPy conveniently allows efficient parallel GPU computing, batched computation of PDEs, and auto-differentiation, without the need for additional loops, data format conversions, or device-to-device transfers. With LA-FEM, the PDE solvers with learnable parameters can be directly integrated into neural network models. Copyright © 2024, The Authors. All rights reserved.

关键词： Convolutional neural networks

Particle shape effect on hydrodynamics and heat transfer in spouted bed:A CFD-DEM study

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Particuology 2022年第10期20卷 10-21页

作者： Dianyu E Peng Zhou Suya Guo Jia Zeng Jiaxin Cui Youyuan Jiang Yuanxiang Lu Zeyi Jiang Zhengquan Li Shibo Kuang Jiangxi Provincial Key Laboratory for Simulation and Modelling of Particulate Systems Jiangxi University of Science and TechnologyGanzhou 341000China Ironmaking Plant Xiangtan Iron and Steel Corporation of Hunan HualingXiangtan 411101China School of Energy and Environmental Engineering University of Science and Technology BeijingBeijing 100083China ARC Research Hub for Computational Particle Technology Department of Chemical EngineeringMonash UniversityClaytonVIC 3800Australia

Spouted bed has drawn much attention due to its good heat and mass transfer efficiency in many chemical *** the flow patterns and heat and mass transfer inside a spouted bed can help optimize the spouting ***,in this study,the effects of particle shape on the hydrodynamics and heat transfer in a spouted bed are *** is done by using a validated computational fluid dynamics-discrete element method(CFD-DEM)model,considering volume-equivalent spheres and oblate and prolate *** results are analysed in detail in terms of the flow pattern,microstruc-ture,and heat transfer *** numerical results show that the prolate spheroids(Ar=2.4)form the largest bubble from the beginning of the spouting process and rise the highest because the fluid drag forces can overcome the interlocking and particle-particle frictional *** with spherical particles,ellipsoidal spheroids have better mobility because of the stronger rotational kinetic energy resulting from the rough surfaces and nonuniform *** addition,the oblate spheroid system exhibits better heat transfer performance benefiting from the larger surface area,while prolate spheroids have poor heat transfer efficiency because of their orientation *** findings can serve as a reference for optimizing the design and operation of complex spouted beds.

关键词： Spouted bed Gas-solid flow Particle shape CFD-DEM Heat transfer

High-density/efficient surface active sites on modified separators to boost Li-S batteries via atomic Co^(3+)-Se termination

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Nano Research 2022年第8期15卷 7199-7208页

作者： Shujie Liu Xiaofei Liu Manfang Chen Dong Wang Xin Ge Wei Zhang Xiyang Wang Chunhui Wang Tingting Qin Haozhe Qin Liang Qiao Dan Zhang Xing Ou Weitao Zheng Key Laboratory of Automobile Materials of MOE School of Materials Science and Engineeringand Electron Microscopy Centerand International Center of Future ScienceJilin UniversityChangchun 130013China Key Laboratory of Materials Design and Quantum Simulation College of ScienceChangchun UniversityChangchun 130022China National Base for International Science&Technology Cooperation School of ChemistryXiangtan UniversityXiangtan 411105China State Key Laboratory of Chem/Bio-Sensing and Chemometrics Advanced Catalytic Engineering Research Center of the Ministry of EducationCollege of Chemistry and Chemical EngineeringHunan UniversityChangsha 410082China Department of Mechanical and Mechatronics Engineering University of WaterlooWaterlooN2L 3G1Canada School of Metallurgy and Environment Central South UniversityChangsha 410083China

Various and critical electrocatalytic processes are involved during the redox reactions in the Li-S batteries,which extremely depend on the surface structure and chemical ***,single-atom concept unlocks a route to maximize the use of surface-active atoms,however,further increasing the density of active site is still strictly limited by the inherent structure that single-atoms are only highly-dispersed on ***,we provide a viewpoint that an elaborate facet design with singlecrystalline structure engineering can harvest high-density surface active sites,which can significantly boost the electrocatalyst performance for excellent Li-S ***,the single-crystal CoSe_(2)(scCS)exhibits three-types of terminated(011)facet,efficiently obtaining the surface with a high-rich Co^(3+)–Se bond termination,in contrast with lots of surface grain boundaries and dangling bonds in polycrystalline CoSe_(2).Surprisingly,the surface active sites concentration can reach more than 69%.As anticipated,it can provide high-density and high-efficient active sites,enormously suppressing the shuttle effect and improving the reaction kinetics via accelerating the conversion and deposition of polysulfides and *** surface lattice strategy with element terminated mode is a promising approach for designing electrocatalyst effect-based energy system,not merely for Li-S batteries.

关键词： high-density surface active sites Co^(3+)-Se covalent bond atomic element terminated Li-S batteries single-crystalline strategy

Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules

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arXiv 2024年

作者： Wang, Xin Shi, An-Chang Zhang, Pingwen Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Department of Physics and Astronomy McMaster University HamiltonONL8S4M1 Canada School of Mathematics and Statistics Wuhan University Wuhan430072 China

Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can result in a great variety of quasicrystals that could be realized by the self-assembly of liquid crystalline molecules. In this study, we introduce three self-similar dodecagonal tilings, including a novel Diamond-Square-Triangle pattern, composed of triangular and quadrangular tiles and examine their thermodynamic stability by using the self-consistent field theory applied to T-shaped liquid crystalline molecules. Specifically, we detail the inflation rules for the construction of these dodecagonal tilings and analyze their self-similarity, and show that these tilings can be viewed as projections of higher-dimensional periodic lattice points with projection windows. Using these dodecagonal tilings as initial configurations of the SCFT results in solutions corresponding to quasicrystals that could form from the T-shaped liquid crystalline molecules. The relative stability of these aperiodic phases is analyzed to obtain design rules that could stabilize quasicrystals. Meanwhile, we provide two criteria for distinguishing three dodecagonal quasicrystals and their approximants by analyzing their diffraction peaks. These findings shed new lighten on the discovery of new quasicrystals in soft materials. Copyright © 2024, The Authors. All rights reserved.

关键词： Quasicrystals