Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method (Q6095431)

scientific article; zbMATH DE number 7735426

Language	Label	Description	Also known as
English	Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method	scientific article; zbMATH DE number 7735426

Statements

instance of

scholarly article

0 references

title

Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method (English)

0 references

0 references

0 references

0 references

SIAM Journal on Scientific Computing

0 references

publication date

8 September 2023

0 references

full work available at URL

https://arxiv.org/abs/2209.02931

0 references

zbMATH Keywords

variable coefficient Poisson equation

0 references

singular source

0 references

deep Ritz method

0 references

penalty method

0 references

neural networks

0 references

MaRDI profile type

MaRDI publication profile

0 references

cites work

Q5318420

0 references

The Gap between Theory and Practice in Function Approximation with Deep Neural Networks

0 references

Introduction to Numerical Continuation Methods

0 references

Neural Network Learning

0 references

A Priori Mesh Grading for an Elliptic Problem with Dirac Right-Hand Side

0 references

Robin Approximation of Dirichlet Boundary Value Problems

0 references

Error-bounds for finite element method

0 references

Optimization Methods for Large-Scale Machine Learning

0 references

A Limited Memory Algorithm for Bound Constrained Optimization

0 references

Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation

0 references

A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities

0 references

A Singularly mixed boundary value problem

0 references

Scientific machine learning through physics-informed neural networks: where we are and what's next

0 references

Finite Element Approximation of Elliptic Problems with Dirac Measure Terms in Weighted Spaces: Applications to One- and Three-dimensional Coupled Problems

0 references

ON THE COUPLING OF 1D AND 3D DIFFUSION-REACTION EQUATIONS: APPLICATION TO TISSUE PERFUSION PROBLEMS

0 references

Neural network approximation

0 references

Convergence Rate Analysis for Deep Ritz Method

0 references

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

0 references

Discretization of Dirac delta functions in level set methods

0 references

Theory and practice of finite elements.

0 references

Q5189317

0 references

On the use of singular functions with finite element approximations

0 references

The extended/generalized finite element method: An overview of the method and its applications

0 references

A Mixed Approach to the Poisson Problem with Line Sources

0 references

Splitting method for elliptic equations with line sources

0 references

Q4275389

0 references

The Green function for uniformly elliptic equations

0 references

Approximation rates for neural networks with encodable weights in smoothness spaces

0 references

On regularizations of the Dirac delta distribution

0 references

A primal dual active set with continuation algorithm for the \(\ell^0\)-regularized optimization problem

0 references

Imaging conductivity from current density magnitude using neural networks*

0 references

\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition

0 references

Optimal A Priori Error Estimates for an Elliptic Problem with Dirac Right-Hand Side

0 references

Properties of Discrete Delta Functions and Local Convergence of the Immersed Boundary Method

0 references

Self-adaptive physics-informed neural networks

0 references

Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations

0 references

Uniform convergence guarantees for the deep Ritz method for nonlinear problems

0 references

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

0 references

A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method

0 references

Finite element convergence for singular data

0 references

Understanding Machine Learning

0 references

DGM: a deep learning algorithm for solving partial differential equations

0 references

Q4614113

0 references

Inverse boundary value problems at the boundary—continuous dependence

0 references

DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations

0 references

Electrical impedance tomography and Calderón's problem

0 references

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

0 references

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

0 references

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

0 references

Error bounds for approximations with deep ReLU networks

0 references

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

0 references

Weak adversarial networks for high-dimensional partial differential equations

0 references

Identifiers

zbMATH Open document ID

0 references

0 references

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:6095431