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Adaptive energy-preserving algorithms for guiding center system

Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

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Fuzzy Filter Design for Affine Systems with Sensor Faults:A Dynamic Event-Triggered Approach

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Journal of Systems Science & Complexity 2022年第5期35卷 1761-1784页

作者： CHENG Jun WU Yuyan WU Zhengguang LI Kezan School of Mathematics and Statistics Center for Applied Mathematics of GuangxiGuangxi Normal Univer-sityGuilin 541006China School of Mathematics and Statistics Guangxi Normal UniversityGuilin 541006China School of Information Science and Engineering Chengdu UniversityChengdu 610106China Institute of Cyber-Systems and Control Zhejiang UniversityHangzhou 310027China School of Mathematics and Computing Science Guilin University of Electronic TechnologyGuilin 541004China

This study addresses the issue of dynamic event-triggered-based filtering for fuzzy affine *** alleviate the utilization of constraint bandwidth resources and improve the efficiency of the signals exchange,a dynamic event-triggered protocol is forwarded to regulate the trigger instants with objective system ***,the nonhomogeneous Markov process is proposed to characterize the dynamic behaviors of sensor faults,where the time-varying transition probabilities belong to a convex polytope ***,the validity and applicability of devised filter design methodology for fuzzy affine systems are displayed via two practical models.

关键词： Dynamic event-triggered protocol fuzzy affine systems nonhomogeneous Markov process sensor fault

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Tensor parametric Hamiltonian operator inference

arXiv

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arXiv 2025年

作者： Vijaywargiya, Arjun McQuarrie, Shane A. Gruber, Anthony Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Computational Mathematics Center for Computing Research Sandia National Laboratories Scientific Machine Learning Center for Computing Research Sandia National Laboratories

This work presents a tensor-based approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with affine dependence as contractions of a generalized parameter vector against a constant tensor, this method leverages the operator inference framework to capture parametric dependence in the learned reduced-order model via the solution to a convex, least-squares optimization problem. This leads to a concise and straightforward implementation which compactifies previous parametric operator inference approaches and directly extends to learning parametric operators with symmetry constraints—a key feature required for constructing structure-preserving surrogates of Hamiltonian systems. The proposed approach is demonstrated on both a (non-Hamiltonian) heat equation with variable diffusion coefficient as well as a Hamiltonian wave equation with variable wave *** Codes 15A69, 35B30, 65P10 © 2025, CC BY.

关键词： Tensors

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EXTENDED GALERKIN NEURAL NETWORK APPROXIMATION OF SINGULAR VARIATIONAL PROBLEMS WITH ERROR CONTROL

arXiv

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arXiv 2024年

作者： Ainsworth, Mark Dong, Justin Division of Applied Mathematics Brown University United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States

We present extended Galerkin neural networks (xGNN), a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs (2) an "extended" feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Numerical results are presented for several problems including steady Stokes flow around re-entrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method. © 2024, CC BY-NC-SA.

关键词： Partial differential equations

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An Improved Super-Resolution Image Reconstruction for Electrical Impedance Tomography

An Improved Super-Resolution Image Reconstruction for Electr...

引用

Machine Learning and Natural Language Processing (MLNLP), International Conference on

作者： Kun Wang Shengwei Teng Siying Lin Keyu Chen Ruwen Zhao School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin China Center for Applied Mathematics of Guangxi (GUET) Guilin China

ISBN: (数字)9798350354973

ISBN: (纸本)9798350354980

Electrical impedance tomography (EIT) is an innovative imaging technique used to recreate the distribution of conductivity in a region by utilizing measured current and voltage readings. In this paper, we introduce a novel method to improve the resolution of EIT images, based on the Efficient Sub-Pixel Convolutional Neural Network (ESPCN). The research involves fine-tuning the parameter weights of the loss function and training the model with datasets of COVID-19 Lung CT Scans Images. The method entails extracting features directly from Low Resolution (LR) images and using convolution operations in sub-pixel convolution layers to accurately capture and reconstruct the morphology and structure of lung tissue. This optimization is designed to solve the two-dimensional forward problem in lung EIT. We propose an Improved Efficient Sub-Pixel Convolutional Neural Network (IESPCN) model to tackle image inverse problems with irregular boundaries. Training the model with unstructured datasets enhances robustness and improves resolution in imaging effects, resulting in high-quality reconstructed images. Experimental results demonstrate that the lung EIT super-resolution reconstruction imaging model based on IESPCN effectively delineates the boundaries of lung organs. This method enhances both the structural fidelity and imaging quality of the output images, while also ensuring stable imaging effects across varying lung boundaries. Furthermore, it improves image resolution and significantly reduces artifacts in the reconstructed images.

关键词： Training Electrical impedance tomography Voltage measurement Convolution Lungs Superresolution Imaging Feature extraction Convolutional neural networks Image reconstruction

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Legendre spectral method for the space-time fractional diffusion-wave equation

Legendre spectral method for the space-time fractional diffu...

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第35届中国控制与决策会议

作者： Huilin Feng Wenping Chen Ying Lu School of Mathematics and Computing Science Guilin University of Electronic Technology Center for Applied Mathematics of Guangxi(GUET)

In this paper,we solve the space-time fractional diffusion-wave equation in a bounded domain by the Legendre spectral *** time fractional derivative is in the Caputo sense with the order γ∈(1,2) and the space fractional derivative is in Riesz *** fully discrete scheme based on the L1 approximation coupled with the Crank-Nicolson technique in temporal and Legendre spectral approximations in spatial discretization are proposed,and the stability and convergence of the fully discrete schemes are *** example is carried out to verify the theoretical results.

关键词：

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AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS

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Journal of Computational mathematics 2021年第6期39卷 848-864页

作者： Liang Yan Tao Zhou School of Mathematics Southeast UniversityNanjing210096China Nanjing Center for Applied Mathematics Nanjing211135China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive forcomplexity problems due to repetitive evaluations of the expensive forward model and itsgradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO. In particular,we propose to drawn the training points for the DNN-surrogate from a local approximatedposterior distribution – yielding a flexible and efficient sampling algorithm that convergesto the direct RTO approach. We present a Bayesian inverse problem governed by ellipticPDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach, which shows that DNN-RTO can significantly outperform the traditional RTO.

关键词： Bayesian inverse problems Deep neural network Markov chain Monte Carlo

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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in Computational Physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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Simulation of the Flow near a Rotating Propeller on Adaptive Unstructured Meshes Using the Immersed Boundary Method

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Mathematical Models and Computer Simulations 2022年第2期14卷 224-240页

作者： Tsvetkova, V.O. Abalakin, I.V. Bobkov, V.G. Zhdanova, N.S. Kozubskaya, T.K. Kudryavtseva, L.N. Keldysh Institute of Applied Mathematics Russian Academy of Sciences Moscow Russian Federation Dorodnitsyn Computing Center Federal Research Center “Computer Science and Control” Russian Academy of Sciences Moscow Russian Federation

Abstract: A method is presented for modeling the flow of a viscous compressible gas around a moving body on a simply connected unstructured mesh, which is possible when using the immersed boundary method, and the features of its application for calculating the flow around a rotating propeller. An important part of the method is the adaptation of a mobile mesh that retains its topology to the surface of the streamlined body. The position and shape of the body are specified by an interpolation mesh, which stores the distance to the body surface and the normal to the surface. The method is used to calculate the flow around a propeller rotating in a flow. The problem is considered in a two-dimensional setting. The shape of the propeller has areas of high curvature that require a special approach when adapting to the boundaries. The results of calculating the problem of the flow around a rotating propeller and a number of auxiliary problems considered in order to verify the developed method are presented. © 2022, Pleiades Publishing, Ltd.

关键词： computational gas dynamics immersed boundary method interpolation mesh mesh adaptation movable mesh rotating propeller unstructured mesh

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Non-Newtonian Effect on Mixed Convection Flow Over an Elliptical Cylinder with Uniform Heat Flux

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International Journal of applied and Computational mathematics 2022年第2期8卷 1-20页

作者： Nag, Preetom Molla, M. Mamun Hossain, M. Anwar Department of Mathematics and Physics North South University Dhaka 1229 Bangladesh Center for Applied Scientific Computing (CASC) North South University Dhaka 1229 Bangladesh Department of Mathematics University of Dhaka Dhaka 1000 Bangladesh

A numerical study about the convective non-Newtonian flow over a cylinder of elliptical cross-sections is conducted with uniform surface heat flux conditions. The non-Newtonian characteristics of the flow are predicted by the empirically defined modified power-law model that has overcome the singularity raised for the original version. The governing non-dimensional boundary layer equations are obtained in non-similar form employing dimensionless transformations. The resulting non-dimensional equations are numerically resolved by using an implicit finite difference scheme for various pertinent parameters. Numerical results have shown that the boundary layer separation over the cylinder is an active function of the mixed convection parameter and the geometry of the cylinder. Besides, the wall shear stress and surface heat transfer rate are investigated as a function of the eccentric angle. The wall shear-stress gets attenuated, and the rate of energy transfer becomes enhanced for non-Newtonian shear-thinning fluids than the Newtonian fluids and shear-thickening fluids. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Boundary layer flow Elliptical cylinder Finite difference method Mixed convection Non-Newtonian fluid Surface heat flux

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