No label defined (Q5104591)

scientific article; zbMATH DE number 7585183

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English	No label defined	scientific article; zbMATH DE number 7585183

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instance of

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15 September 2022

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full work available at URL

https://www.global-sci.org/intro/article_detail/ijnam/20929.html

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zbMATH Keywords

coupled hyperbolic/wave equations

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Korteweg-de Vries (KdV) equations

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Klein-Gordon (KG) equations

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deep neural network (DNN)

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finite element method (FEM)

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space-time sample points (training) set

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least-squares (LS)

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convergence accuracy

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energy conservation

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describes a project that uses

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MaRDI publication profile

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cites work

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Multi-solitons for nonlinear Klein–Gordon equations

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Applications of KdV

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Nonlinear approximation and (deep) ReLU networks

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The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions

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The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations

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The Speed of Mean Glivenko-Cantelli Convergence

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On the rate of convergence in Wasserstein distance of the empirical measure

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Q5270493

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Solving high-dimensional partial differential equations using deep learning

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Energy-preserving finite element methods for a class of nonlinear wave equations

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Convergence of a full discrete finite element method for the Korteweg-de Vries equation

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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

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Approximation rates for neural networks with general activation functions

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DGM: a deep learning algorithm for solving partial differential equations

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Topological soliton solution and bifurcation analysis of the Klein-Gordon-Zakharov equation in \((1 + 1)\)-dimensions with power law nonlinearity

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Singular solitons and bifurcation analysis of quadratic nonlinear Klein-Gordon equation

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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

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Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

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A Local Discontinuous Galerkin Method for KdV Type Equations

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Weak adversarial networks for high-dimensional partial differential equations

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A generalized auxiliary equation method and its application to \((2+1)\)-dimensional Korteweg-de Vries equations

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Deep distributed convolutional neural networks: Universality

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Identifiers

Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:5104591