Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations

Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (1)

Local randomized neural networks with discontinuous Galerkin methods for diffusive-viscous wave equation

Cites Work

Unnamed Item
Unnamed Item
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Weak adversarial networks for high-dimensional partial differential equations
Approximation and estimation bounds for artificial neural networks
Some observations on Babuška and Brezzi theories
One-dimensional linear advection-diffusion equation: analytical and finite element solutions
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
DGM: a deep learning algorithm for solving partial differential equations
Approximation rates for neural networks with encodable weights in smoothness spaces
nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries
Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation
MIM: a deep mixed residual method for solving high-order partial differential equations
Variational physics informed neural networks: the role of quadratures and test functions
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
BCR-net: A neural network based on the nonstandard wavelet form
PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
Error bounds for approximations with deep ReLU networks
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Solving for high-dimensional committor functions using artificial neural networks
The finite element method with Lagrangian multipliers
Relu Deep Neural Networks and Linear Finite Elements
Solving high-dimensional partial differential equations using deep learning
Optimal Approximation with Sparsely Connected Deep Neural Networks
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
fPINNs: Fractional Physics-Informed Neural Networks
Approximation by superpositions of a sigmoidal function

This page was built for publication: Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations