Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms (Q6087958)

scientific article; zbMATH DE number 7766245

Language	Label	Description	Also known as
English	Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms	scientific article; zbMATH DE number 7766245

Statements

instance of

scholarly article

0 references

title

Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms (English)

0 references

arXiv ID

2303.12245

0 references

DOI

10.1016/j.jcp.2023.112527

0 references

0 references

0 references

0 references

0 references

Journal of Computational Physics

0 references

publication date

16 November 2023

0 references

full work available at URL

https://arxiv.org/abs/2303.12245

0 references

Mathematics Subject Classification ID

0 references

0 references

PINN

0 references

neural network

0 references

error estimate

0 references

PDE

0 references

scientific machine learning

0 references

MaRDI profile type

MaRDI publication profile

0 references

cites work

High-order discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes

0 references

Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs

0 references

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

0 references

Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

0 references

Error estimates for deep learning methods in fluid dynamics

0 references

Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs

0 references

Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients

0 references

Deep Learning Architectures

0 references

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

0 references

Q3510853

0 references

On the approximation of functions by tanh neural networks

0 references

Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

0 references

Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions

0 references

Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

0 references

A modified batch intrinsic plasticity method for pre-training the random coefficients of extreme learning machines

0 references

A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

0 references

Numerical approximation of partial differential equations by a variable projection method with artificial neural networks

0 references

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

0 references

Deep Neural Network Approximation Theory

0 references

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines

0 references

MgNet: a unified framework of multigrid and convolutional neural network

0 references

Higher-order error estimates for physics-informed neural networks approximating the primitive equations

0 references

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

0 references

Classical elastodynamics as a linear symmetric hyperbolic system

0 references

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

0 references

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

0 references

Q2748316

0 references

DeepXDE: A Deep Learning Library for Solving Differential Equations

0 references

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

0 references

Estimates on the generalization error of physics-informed neural networks for approximating PDEs

0 references

Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences

0 references

Generalization bounds for function approximation from scattered noisy data

0 references

Q5491447

0 references

A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions

0 references

Meta-learning PINN loss functions

0 references

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

0 references

Global existence of small solutions to nonlinear evolution equations

0 references

Normal forms and quadratic nonlinear Klein-Gordon equations

0 references

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

0 references

Greedy training algorithms for neural networks and applications to PDEs

0 references

DGM: a deep learning algorithm for solving partial differential equations

0 references

Infinite-dimensional dynamical systems in mechanics and physics.

0 references

VAE-KRnet and Its Applications to Variational Bayes

0 references

Classical Global Solutions for Non-linear Klein-Gordon-Schrödinger Equations

0 references

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

0 references

Q5531981

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:6087958