A deep Fourier residual method for solving PDEs using neural networks (Q2683430)

scientific article; zbMATH DE number 7653051

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English	A deep Fourier residual method for solving PDEs using neural networks	scientific article; zbMATH DE number 7653051

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instance of

scholarly article

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title

A deep Fourier residual method for solving PDEs using neural networks (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

10 February 2023

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full work available at URL

https://arxiv.org/abs/2210.14129

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zbMATH Keywords

deep learning

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neural networks

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numerical PDEs

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Fourier methods

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describes a project that uses

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A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Deep neural networks motivated by partial differential equations

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An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications

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Approximation by superpositions of a sigmoidal function

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Q4558473

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Large-Scale Machine Learning with Stochastic Gradient Descent

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Universal approximation bounds for superpositions of a sigmoidal function

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A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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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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DGM: a deep learning algorithm for solving partial differential equations

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On quadrature rules for solving partial differential equations using neural networks

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Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection-diffusion-reaction problems

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Solving PDEs by variational physics-informed neural networks: an a posteriori error analysis

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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

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The finite cell method for three-dimensional problems of solid mechanics

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Distributed Lagrange multipliers based on fictitious domain method for second order elliptic problems

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The finite cell method with least squares stabilized Nitsche boundary conditions

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IMMERSED BOUNDARY METHODS

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The immersed boundary method

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A fictitious domain approach with spread interface for elliptic problems with general boundary conditions

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The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models

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On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors

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Q5301029

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A finite element based deep learning solver for parametric PDEs

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When and why PINNs fail to train: a neural tangent kernel perspective

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Spectral Methods

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Computing with hp-ADAPTIVE FINITE ELEMENTS

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Functional analysis, Sobolev spaces and partial differential equations

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CMA.2022.115850

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Sitelinks

Mathematics(1 entry)

mardi Publication:2683430