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检索条件："刊名=Communications on Applied Mathematics and Computation "
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Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method
《Communications on Applied Mathematics and Computation》2024年第2期1070-1095,共26页Guanghui Huang Jianliang Qian Yang Yang 
partially supported by the NSF(Grant Nos.2012046,2152011,and 2309534);partially supported by the NSF(Grant Nos.DMS-1715178,DMS-2006881,and DMS-2237534);NIH(Grant No.R03-EB033521);startup fund from Michigan State University.
We investigate the following inverse problem:starting from the acoustic wave equation,reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of s...
关键词：Inverse gravimetry Acoustic source imaging Inversion of sound speed Level-set method Inverse problem 
Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations
《Communications on Applied Mathematics and Computation》2024年第2期1096-1130,共35页Zhanhong Ye Xiang Huang Hongsheng Liu Bin Dong 
supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...
关键词：Parametric partial differential equations(PDEs) META-LEARNING Reduced order modeling Neural networks(NNs) Auto-decoder 
Nearest Neighbor Sampling of Point Sets Using Rays
《Communications on Applied Mathematics and Computation》2024年第2期1131-1174,共44页Liangchen Liu Louis Ly Colin B.Macdonald Richard Tsai 
supported by the National Science Foundation(Grant No.DMS-1440415);partially supported by a grant from the Simons Foundation,NSF Grants DMS-1720171 and DMS-2110895;a Discovery Grant from Natural Sciences and Engineering Research Council of Canada.
We propose a new framework for the sampling,compression,and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces.Our approach involves constructing a tensor called the RaySe...
关键词：Point clouds Sampling CLASSIFICATION REGISTRATION Deep learning Voronoi cell analysis 
Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
《Communications on Applied Mathematics and Computation》2024年第2期1175-1188,共14页Wes Whiting Bao Wang Jack Xin 
partially supported by NSF Grants DMS-1854434,DMS-1952644,and DMS-2151235 at UC Irvine;supported by NSF Grants DMS-1924935,DMS-1952339,DMS-2110145,DMS-2152762,and DMS-2208361,and DOE Grants DE-SC0021142 and DE-SC0002722.
We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a ...
关键词：Hyperbolic neural network Riemannian gradient descent Riemannian Adam(RAdam) Training convergence 
A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem onImplicit Surfaces
《Communications on Applied Mathematics and Computation》2024年第2期1189-1216,共28页Young Kyu Lee Shingyu Leung 
supported in part by the Hong Kong RGC 16302223.
We propose a simple embedding method for computing the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on implicit surfaces.The approach follows an embedding approach for solving the surface eikonal eq...
关键词：Laplace-Beltrami operator Level set method Implicit representation EIGENVALUES Numerical PDEs 
A Space-Time Interior Penalty Discontinuous Galerkin Method for the Wave Equation
《Communications on Applied Mathematics and Computation》2022年第3期904-944,共41页Poorvi Shukla J.J.W.van der Vegt 
A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order...
关键词：Wave equation Space-time methods Discontinuous Galerkin methods Interior penalty method A priori error analysis 
Optimization in Machine Learning:a Distribution-Space Approach
《Communications on Applied Mathematics and Computation》2024年第2期1217-1240,共24页Yongqiang Cai Qianxiao Li Zuowei Shen 
supported by the National Natural Science Foundation of China(Grant No.12201053);supported by the National Research Foundation,Singapore,under the NRF fellowship(Project No.NRF-NRFF13-2021-0005).
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space,but with a non-convex constraint set introduced by m...
关键词：Machine learning Convex relaxation OPTIMIZATION Distribution space 
Von Neumann Stability Analysis of DG-Like and PNPM-Like Schemes for PDEs with Globally Curl-Preserving Evolution of Vector Fields
《Communications on Applied Mathematics and Computation》2022年第3期945-985,共41页Dinshaw S.Balsara Roger Käppeli 
Open Access funding provided by ETH Zurich.The funding has been acknowledged.DSB acknowledges support via NSF grants NSF-19-04774,NSF-AST-2009776 and NASA-2020-1241.
This paper examines a class of involution-constrained PDEs where some part of the PDE system evolves a vector field whose curl remains zero or grows in proportion to specified source terms.Such PDEs are referred to as...
关键词：PDES Numerical schemes MIMETIC Discontinuous Galerkin 
Adaptive State-Dependent Diffusion for Derivative-Free Optimization
《Communications on Applied Mathematics and Computation》2024年第2期1241-1269,共29页Bjorn Engquist Kui Ren Yunan Yang 
partially supported by the National Science Foundation through grants DMS-2208504(BE),DMS-1913309(KR),DMS-1937254(KR),and DMS-1913129(YY);support from Dr.Max Rossler,the Walter Haefner Foundation,and the ETH Zurich Foundation.
This paper develops and analyzes a stochastic derivative-free optimization strategy.A key feature is the state-dependent adaptive variance.We prove global convergence in probability with algebraic rate and give the qu...
关键词：Derivative-free optimization Global optimization Adaptive diffusion Stationary distribution Fokker-Planck theory 
Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks
《Communications on Applied Mathematics and Computation》2022年第3期986-1010,共25页LukášVacek Václav Kučera 
The work of L.Vacek is supported by the Charles University,project GA UK No.1114119;The work of V.Kučera is supported by the Czech Science Foundation,project No.20-01074S.
In this paper,we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads.On individual roads,we consider the standard Lighthill-Whitham-Richards model which is discretiz...
关键词：Traffic flow Conservations laws on networks Discontinuous Galerkin method Numerical flux 
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