检索结果-内蒙古大学图书馆

Stochastic Trust-Region Methods with Trust-Region Radius Depending on Probabilistic Models

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Wang, Xiaoyu Yuan, Ya-Xiang Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the latest model gradient. The complexity of STRME method in non-convex, convex and strongly convex settings has all been analyzed, which matches the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient *** Codes 65K05, 65K10, 90C60 Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Hu, Mengqi Lou, Yifei Wang, Bao Yan, Ming Yang, Xiu Ye, Qiang Department of Industrial and Systems Engineering Lehigh University 200 West Packer Avenue BethlehemPA18015 United States Department of Mathematical Sciences The University of Texas at Dallas 800 W. Campbell Rd RichardsonTX75080 United States Department of Mathematics and Scientific Computing Imaging Institute The University of Utah 72 Central Campus Dr Salt Lake CityUT84102 United States School of Data Science The Chinese University of Hong Kong Shenzhen 2001 Longxiang Blvd Guangdong Shenzhen China Department of Computational Mathematics Science and Engineering Department of Mathematics Michigan State University 428 South Shaw Lane East LansingMI48824 United States Department of Mathematics University of Kentucky LexingtonKY40513 United States

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex 1 and the nonconvex 1 − 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods. © 2022, CC BY-SA.

关键词： Momentum

An Energy Stable Linear Diffusive Crank-Nicolson Scheme for the Cahn-Hilliard Gradient Flow

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Wang, Lin Yu, Haijun School of Applied Mathematics Guangdong University of Technology GuangzhouGuangdong510006 China LSEC & NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose and analyze a linearly stabilized semi-implicit diffusive Crank–Nicolson scheme for the Cahn–Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic system with constant coefficients and provable discrete energy dissipation. Rigorous error analysis is carried out for the fully discrete scheme. When the time step-size and the space step-size are small enough, second order accuracy in time is obtained with a prefactor controlled by some lower degree polynomial of 1/Ε. Here Ε is the thickness of the interface. Numerical results together with an adaptive time stepping are presented to verify the accuracy and efficiency of the proposed scheme. Copyright © 2020, The Authors. All rights reserved.

关键词： Error analysis

Redefining pandemic preparedness:Multidisciplinary insights from the CERP modelling workshop in infectious diseases,workshop report

学校读者我要写书评

暂无评论

Infectious Disease Modelling 2024年第2期9卷 501-518页

作者： Marta C.Nunes Edward Thommes Holger Fröhlich Antoine Flahault Julien Arino Marc Baguelin Matthew Biggerstaff Gaston Bizel-Bizellot Rebecca Borchering Giacomo Cacciapaglia Simon Cauchemez Alex Barbier-Chebbah Carsten Claussen Christine Choirat Monica Cojocaru Catherine Commaille-Chapus Chitin Hon Jude Kong Nicolas Lambert Katharina B.Lauer Thorsten Lehr Cédric Mahe Vincent Marechal Adel Mebarki Seyed Moghadas Rene Niehus Lulla Opatowski Francesco Parino Gery Pruvost Andreas Schuppert Rodolphe Thiébaut Andrea Thomas-Bachli Cecile Viboud Jianhong Wu Pascal Crépey Laurent Coudeville Center of Excellence in Respiratory Pathogens(CERP) Hospices Civils de Lyon(HCL)and Centre International de Recherche en Infectiologie(CIRI)Équipe SantéPubliqueÉpidémiologie etÉcologieÉvolutive des Maladies Infectieuses(PHE3ID)Inserm U1111CNRS UMR5308ENS de LyonUniversitéClaude Bernard Lyon 1LyonFrance South African Medical Research Council Vaccines&Infectious Diseases Analytics Research UnitFaculty of Health SciencesUniversity of the WitwatersrandJohannesburgSouth Africa New Products and Innovation(NPI) Sanofi Vaccines(Global)TorontoOntarioCanada Department of Mathematics and Statistics University of GuelphGuelphOntarioCanada Fraunhofer Institute for Algorithms and Scientific Computing(SCAI) Department of BioinformaticsSchloss BirlinghovenSankt AugustinGermany University of Bonn Bonn-Aachen International Center for IT(b-it)BonnGermany Institute of Global Health Faculty of MedicineUniversity of GenevaGenevaSwitzerland and Swiss School of Public HealthZürichSwitzerland Department of Mathematics University of ManitobaWinnipegManitobaCanada MRC Centre for Global Infectious Disease Analysis School of Public HealthImperial College LondonLondonUK Centre for Mathematical Modelling of Infectious Diseases Department of Infectious Disease EpidemiologyLondon School of Hygiene&Tropical MedicineLondonUK National Center for Immunization and Respiratory Diseases(NCIRD) US Centers for Disease Control and Prevention(CDC)AtlantaGAUSA Departement of Computational Biology Departement of Global HealthInstitut PasteurParisFrance Institut de Physique des Deux Infinis de Lyon(IP2I) UMR5822IN2P3/CNRSUniversitéClaude Bernard Lyon 1VilleurbanneFrance Mathematical Modelling of Infectious Diseases Unit Institut PasteurUniversitéParis CitéUMR2000 CNRSParisFrance Decision and Bayesian Computation Institut PasteurUniversitéParis CitéCNRS UMR 3571France Fraunhofer-Institute for Translational Medicine and Pharmacology HamburgGermany Institute of Global Health Faculty of MedicineUniversity of

In July 2023,the Center of Excellence in Respiratory Pathogens organized a two-day workshop on infectious diseases modelling and the lessons learnt from the Covid-19 *** report summarizes the rich discussions that occurred during the *** workshop participants discussed multisource data integration and highlighted the benefits of combining traditional surveillance with more novel data sources like mobility data,social media,and wastewater *** advancements were noted in the development of predictive models,with examples from various countries showcasing the use of machine learning and artificial intelligence in detecting and monitoring disease *** role of open collaboration between various stakeholders in modelling was stressed,advocating for the continuation of such partnerships beyond the pandemic.A major gap identified was the absence of a common international framework for data sharing,which is crucial for global pandemic ***,the workshop underscored the need for robust,adaptable modelling frameworks and the integration of different data sources and collaboration across sectors,as key elements in enhancing future pandemic response and preparedness.

关键词： Modelling Covid-19 Infectious diseases Pandemic preparedness Workshop

A plane wave study on the localized-extended transitions in the one-dimensional incommensurate systems

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Chen, Huajie Zhou, Aihui Zhou, Yuzhi School of Mathematical Sciences Beijing Normal University Beijing100875 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Software Center for High Performance Numerical Simulation China Academy of Engineering Physics Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent experiments in the ultracold atom and photonic crystal. We formulate a propagator based scattering picture for the transition at the ground state and single particle mobility edge, in which the deeper connection between the incommensurate potentials, eigenstate compositions and transition mechanism is revealed. We further show that there exists a upper limit of localization length for all localized eigenstates, leading to an fundamental difference to the Anderson localization. Numerical calculations are presented alongside the analysis to justify our statements. The theoretical analysis and numerical methods can also be generalized to systems in higher dimensions, with different potentials or beyond the single particle regime, which would benefit the future studies in the related fields. Copyright © 2020, The Authors. All rights reserved.

关键词： Elastic waves

Large strain constitutive modelling of soft compressible and incompressible solids: Generalised isotropic and anisotropic viscoelasticity

学校读者我要写书评

暂无评论

Journal of the Mechanics and Physics of Solids 2025年 203卷

作者： Zeng Liu Rogelio Ortigosa Antonio J. Gil Javier Bonet Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE) Barcelona Spain Departament de Enginyeria Civil i Ambiental (DECA) Universitat Politècnica de Catalunya Barcelona Spain Computational Mechanics and Scientific Computing Group Technical University of Cartagena Campus Muralla del Mar 30202 Cartagena (Murcia) Spain Zienkiewicz Institute for Modelling Data and AI Faculty of Science and Engineering Swansea University Bay Campus SA1 8EN United Kingdom

This paper discusses a new phenomenological continuum formulation for the constitutive modelling of viscoelastic materials at large strains. Following pioneering works in Sidoroff (1974), Lubliner (1985), Bergström (1998) and Reese and Govindjee (1997), the formulation shares some common ingredients with other phenomenological approaches, including the multiplicative decomposition of the deformation gradient into viscous and elastic contributions, the additive Maxwell-type decomposition of the strain energy density, and the definition of a set of kinematic internal state variables with their associated evolution laws. Our formulation departs from other state-of-the-art methodologies via three distinct novelties. First, and revisiting previous work by Bonet (2001), the paper introduces a thermodynamically consistent linear rate type evolution law in terms of stress-type variables, which resembles the return mapping algorithm typically used in elastoplasticity, facilitating the modelling link between both inelastic constitutive models. In this sense, the proposed viscoelastic evolution law can be identified with a classical plastic flow rule. Very importantly, the evolution law is shown to be compatible with the second law of thermodynamics by construction and have a closed-form solution in the case of incompressible viscoelasticity when using a prototypical neo-Hookean type of non-equilibrium strain energy density. Moreover, the paper shows how using the concept of a stress-driven dissipative potential, more general non-linear type of stress evolution laws can be straightforwardly constructed. Second, to facilitate the joint consideration of anisotropy and thermodynamic equilibrium, a frame indifferent stress free configuration is introduced which facilitates the definition of objective strain measures. Third, the methodology is extended from isotropy to transverse isotropy via the consideration of the appropriate structural tensor. The formulation is first displayed

关键词： Large strain Finite viscoelasticity Maxwell rheological model Multiplicative decomposition

A DISCONTINUOUS GALERKIN METHOD BY PATCH RECONSTRUCTION FOR BIHARMONIC PROBLEM

学校读者我要写书评

暂无评论

Journal of computational mathematics 2019年第4期37卷 524-540页

作者： Ruo Li Pingbing Ming Zhiyuan Sun Fanyi Yang Zhijian Yang CAPT LMAM and School of Mathematical Sciences Peking University Beijing 100871 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences No. 19A Yu-Quan Road Beijing 100049 China School of Mathematical Sciences Peking University Beijing 100871 China School of Mathematics and. Statistics Wuhan University Wuhan 430072 China

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

关键词： Least-squares problem Reconstructed basis function Discontinuous Galerkin method Biharmonic problem

Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China Division of Science and Technology BNU-HKBU United International College ZhuhaiGuangdong Province China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysis tool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators. More precisely, for a class of discrete convolution kernels relevant to variable-step time discretizations, we show that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Our proof is based on an elementary constructing strategy using the properties of discrete orthogonal convolution kernels and complementary convolution kernels. To the best of our knowledge, this is the first general result on simple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using the unified theory, the stability for some simple non-uniform time-stepping schemes can be obtained in a straightforward *** Codes 65M06, 65M12, 65R20. © 2020, CC BY-NC-SA.

关键词： Number theory

ParaDiag: Parallel-in-time algorithms based on the diagonalization technique

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Gander, Martin J. Liu, Jun Wu, Shu-Lin Yue, Xiaoqiang Zhou, Tao Section of Mathematics University of Geneva GenevaCH-1211 Switzerland Department of Mathematics and Statistics Southern Illinois University Edwardsville EdwardsvilleIL62026 United States School of Mathematics and Statistics Northeast Normal University Changchun130024 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

In 2008, Maday and Rønquist introduced an interesting new approach for the direct parallel-in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepping matrix, keeping the matrices for the space discretization unchanged, and then to solve all time steps in parallel. Since then, several variants appeared, and we call these closely related algorithms ParaDiag algorithms. ParaDiag algorithms in the literature can be classified into two groups: We will explain the basic features of each group in this note. To have concrete examples, we will introduce ParaDiag-I and ParaDiag-II for the advection-diffusion equation. We will also introduce ParaDiag-II for the wave equation and an optimal control problem for the wave equation. We could have used the advection-diffusion equation as well to illustrate ParaDiag-II, but wave equations are known to cause problems for certain PinT algorithms and thus constitute an especially interesting example for which ParaDiag algorithms were tested. We show the main known theoretical results in each case, and also provide Matlab codes for testing. The goal of the Matlab codes is to help the interested reader understand the key features of the ParaDiag algorithms, without intention to be highly tuned for efficiency and/or low memory use. We also provide speedup measurements of ParaDiag algorithms for a 2D linear advection-diffusion equation. These results are obtained on the Tianhe-1 supercomputer in China and the SIUE Campus Cluster in the US, which is a multi-array, configurable and cooperative parallel system, and we compare these results to the performance of parareal and MGRiT, two widely used PinT algorithms. In a forthcoming update of this note, we will provide more material on ParaDiag algorithms, in particular further Matlab codes and parallel computing results, also for more realistic applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Advection