MIM: a deep mixed residual method for solving high-order partial differential equations (Q2133607)

scientific article; zbMATH DE number 7517751

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English	MIM: a deep mixed residual method for solving high-order partial differential equations	scientific article; zbMATH DE number 7517751

Statements

instance of

scholarly article

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title

MIM: a deep mixed residual method for solving high-order partial differential equations (English)

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Journal of Computational Physics

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publication date

4 May 2022

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full work available at URL

https://arxiv.org/abs/2006.04146

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zbMATH Keywords

high-order partial differential equations

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deep learning

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deep mixed residual method

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deep Galerkin method

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describes a project that uses

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Finite Elements and Fast Iterative Solvers

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Q4952239

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Spectral Methods

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Q3391630

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Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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Q4794126

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Solving the quantum many-body problem with artificial neural networks

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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Solving high-dimensional partial differential equations using deep learning

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Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

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DGM: a deep learning algorithm for solving partial differential equations

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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

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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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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

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A Multiscale Neural Network Based on Hierarchical Matrices

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Solving for high-dimensional committor functions using artificial neural networks

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Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations

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Deep multiscale model learning

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Weak adversarial networks for high-dimensional partial differential equations

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Controlling oscillations in high-order discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

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Solving many-electron Schrödinger equation using deep neural networks

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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

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Mixed Finite Element Methods and Applications

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Local discontinuous Galerkin methods for partial differential equations with higher order derivatives

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A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems

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Q5491028

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A weak Galerkin finite element method with polynomial reduction

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A Comparison Study of Deep Galerkin Method and Deep Ritz Method for Elliptic Problems with Different Boundary Conditions

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Updating Quasi-Newton Matrices with Limited Storage

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Relu Deep Neural Networks and Linear Finite Elements

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2021.110930

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Sitelinks

Mathematics(1 entry)

mardi Publication:2133607