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ASME 2024 International Mechanical engineering Congress and Exposition, IMECE 2024

作者： Wang, Yunchu Wang, Yize Yuan, Li NCMIS 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

ISBN: (纸本)9780791888667

Quadrature-based moment methods (QBMMs) are an alternative approach for the numerical solution of the probability density function (PDF) model equation for turbulent combustion. In this work, we propose a new QBMM called Linear Quadrature Method Of Moments (LQMOM) for the univariate PDF case. We use a set of predefined quadrature nodes and weights in the sample space to establish linear equations for the PDF values at the nodes in the moment inversion. The LQMOM is more economic than the original QMOM which needs to solve nonlinear equations in the moment inversion. However, the LQMOM may return negative PDF values for a non-smooth PDF. So we construct the LQMOM-QMOM hybrid algorithm. Further, we develop the linear Conditional Quadrature Method Of Moments (LCQMOM) and a simplified version (LCQMOM-S) for the multivariate PDF case by referring to the main idea of the original CQMOM. The LQMOM-QMOM hybrid algorithm is tested in a plug-flow reactor example, and the LQMOM(-S)-CQMOM hybrid algorithms in conjunction with a LES method are tested in two compressible turbulent reactive flow examples. The numerical results show that the hybrid algorithms can reduce 20-35% computational cost compared with the respective QMOM and CQMOM. Copyright © 2024 by ASME.

关键词： Probability density function

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A two-dimensional double layer-averaged model of hyperconcentrated turbidity currents with non-Newtonian rheology

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International Journal of Sediment Research 2023年第6期38卷 794-810页

作者： Yining Sun Ji Li Zhixian Cao Alistair George Liam Borthwick State Key Laboratory of Water Resources Engineering and Management Wuhan University Zienkiewicz Centre for Computational Engineering Faculty of Science and EngineeringSwansea University Institute for Infrastructure and Environment University of Edinburgh School of Engineering Computing and MathematicsUniversity of Plymouth

Hyperconcentrated turbidity currents typically display non-Newtonian characteristics that influence sediment transport and morphological evolution in alluvial ***,hydro-sedimentmorphological processes involving hyperconcentrated turbidity currents are poorly understood,with little known about the effect of the non-Newtonian *** current paper extends a recent twodimensional double layer-averaged model to incorporate non-Newtonian constitutive *** extended model is benchmarked against experimental and numerical data for cases including subaerial mud flow,subaqueous debris flow,and reservoir turbidity *** computational results agree well with observations for the subaerial mud flow and independent numerical simulations of subaqueous debris *** between the non-Newtonian and Newtonian model results become more pronounced in terms of propagation distance and sediment transport rate as sediment concentration *** model is then applied to turbidity currents in the Guxian Reservoir planned for middle Yellow River,China,which connects to a tributary featuring hyperconcentrated sediment-laden *** non-Newtonian model predicts slower propagation of turbidity currents and more significant bed aggradation at the confluence between the tributary Wuding River and the Yellow River in the reservoir than its Newtonian *** difference in model performance could be of considerable importance when optimizing reservoir operation schemes.

关键词： Double layer-averaged model Non-Newtonian rheology Mud flow Reservoir turbidity current Yellow River

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DISCRETE ENERGY ANALYSIS OF THE THIRD-ORDER VARIABLE-STEP BDF TIME-STEPPING FOR DIFFUSION EQUATIONS

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Journal of computational mathematics 2023年第2期41卷 325-344页

作者： Hong-lin Liao Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

This is one of our series works on discrete energy analysis of the variable-step BDF *** this part,we present stability and convergence analysis of the third-order BDF(BDF3)schemes with variable steps for linear diffusion equations,see,e.g.,[SIAM ***.,58:2294-2314]and[***.,90:1207-1226]for our previous works on the BDF2 *** this aim,we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877,by which we can establish a discrete energy dissipation ***-robust stability and convergence analysis in the L^(2) norm are then *** the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step *** also present numerical tests to support our theoretical results.

关键词： Diffusion equations Variable-step third-order BDF scheme Discrete gradient structure Discrete orthogonal convolution kernels Stability and convergence

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A NEW ADAPTIVE SUBSPACE MINIMIZATION THREE-TERM CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

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Journal of computational mathematics 2021年第2期39卷 159-177页

作者： Keke Zhang Hongwei Liu Zexian Liu School of Mathematics and Statistics Xidian UniversityXi’an 710126China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computingAMSSChinese Academy of SciencesBeijing 100190China

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this *** search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces,and we also proposed an adaptive rule for choosing different searching directions at each *** obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent *** the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functions under some mild *** experiments show that the proposed algorithm is promising for the given test problem set.

关键词： Conjugate gradient method Nonmonotone line search Subspace minimization Sufficient descent condition Global convergence

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A Riemannian Exponential Augmented Lagrangian Method for computing the Projection Robust Wasserstein Distance 37

A Riemannian Exponential Augmented Lagrangian Method for Com...

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37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Jiang, Bo Liu, Ya-Feng Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

ISBN: (纸本)9781713899921

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the stepsizes in efforts as done in the existing methods. We show that iRBBS can return an Ε-stationary point of the original PRW distance problem within O(Ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Constrained optimization

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An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

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Communications in computational Physics 2022年第3期31卷 966-986页

作者： Jianguo Huang Haoqin Wang Tao Zhou School of Mathematical Sciences and MOE-LSCShanghai Jiao Tong UniversityShanghaiChina LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

This paper is concerned with a novel deep learning method for variational problems with essential boundary *** this end,wefirst reformulate the original problem into a minimax problem corresponding to a feasible augmented La-grangian,which can be solved by the augmented Lagrangian method in an infinite dimensional *** on this,by expressing the primal and dual variables with two individual deep neural network functions,we present an augmented Lagrangian deep learning method for which the parameters are trained by the stochastic optimiza-tion method together with a projection *** to the traditional penalty method,the new method admits two main advantages:i)the choice of the penalty parameter isflexible and robust,and ii)the numerical solution is more accurate in the same magnitude of computational *** typical applications,we apply the new ap-proach to solve elliptic problems and(nonlinear)eigenvalue problems with essential boundary conditions,and numerical experiments are presented to show the effective-ness of the new method.

关键词： The augmented Lagrangian method deep learning variational problems saddle point problems essential boundary conditions

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Unifying AMP Algorithms for Rotationally-Invariant Models

arXiv

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arXiv 2024年

作者： Liu, Songbin Ma, Junjie The Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP (OAMP), we systematically derive the correct Onsager terms of AMP algorithms. This approach allows us to rederive an AMP algorithm introduced by Fan and Opper et al., while shedding new light on the role of free cumulants of the spectral law. The free cumulants arise naturally from a recursive centering operation, potentially of independent interest beyond the scope of AMP. To illustrate the flexibility of our framework, we introduce two novel AMP variants and apply them to estimation in spiked models. © 2024, CC BY.

关键词： Consensus algorithm

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A Variational Approach to Personalized Federated Learning and Its Improvement 20th

A Variational Approach to Personalized Federated Learning a...

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20th Principle and Practice of Data and Knowledge Acquisition Workshop, PKAW 2024, held in conjunction with the 21st Pacific Rim International Conference on Artificial Intelligence, PRICAI 2024

作者： Wu, Huiwen Zhang, Shuo Research Center for Data Hub and Security Zhejiang Laboratory Hangzhou310000 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

ISBN: (纸本)9789819600250

Federated learning (FL) is a new approach that allows clients from different locations to work together on a global model without sharing raw data. However, training one standard model is not optimal for local optimization due to heterogeneity. Thus, personalized federated learning (PFL) paradigms aim to combine local and global information while preserving diversity among local clients. However, these methods require more theoretical motivation. This paper formalizes the unfired analysis form by defining a linear mapping on the server’s aggregation step for a deeper understanding of the implementation design and to improve existing methods further. Moreover, we show that the existing FL and PFL methods are specific cases in our framework with selected mapping matrices, including FedAvg, FedMTL, FedProx, MAML, and pure local training. Based on that, we propose a novel data-driven graph Laplacian-induced PFL scheme named GLIP-FL to address statistical heterogeneity issues and improve computation efficiency. We implement evaluation experiments of the proposed method on four popular data sets with five FL baselines in three data partitions, both homogeneous and heterogeneous, and the comprehensive experiments show the great potential of our method. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Federated learning

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Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

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Communications on Applied mathematics and Computation 2024年第1期6卷 30-63页

作者： Maohui Lyu Vrushali A.Bokil Yingda Cheng Fengyan Li State Key Laboratory of Scientific and Engineering Computing(LSEC) Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing100190China Department of Mathematics College of ScienceOregon State UniversityCorvallisOR97331USA Department of Mathematics Michigan State UniversityEast LansingMI48824USA Department of Computational Mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA Department of Mathematical Sciences Rensselaer Polytechnic InstituteTroyNY12180USA

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational *** the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the *** main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order *** with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel *** evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

关键词： Maxwell’s equations Kerr and Raman Discontinuous Galerkin method Energy stability

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Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments

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Numerical mathematics(Theory,Methods and Applications) 2021年第1期14卷 194-218页

作者： Yidan Geng Minghui Song Yulan Lu Mingzhu Liu Department of Mathematics Harbin Institute of TechnologyHarbin 150001China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type *** order of convergence is ***,we show that the truncated EM method can preserve the exponential mean square stability of *** examples are provided to support our conclusions.

关键词： Stochastic differential equations with piecewise continuous argument local Lips-chitz condition Khasminskii-type condition truncated Euler-Maruyama method convergence and stability

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