Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms
From MaRDI portal
Publication:6087958
DOI10.1016/j.jcp.2023.112527arXiv2303.12245MaRDI QIDQ6087958
Yunqing Huang, Yanxia Qian, Yong-Chao Zhang, Suchuan Dong
Publication date: 16 November 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2303.12245
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Global existence of small solutions to nonlinear evolution equations
- Classical elastodynamics as a linear symmetric hyperbolic system
- Generalization bounds for function approximation from scattered noisy data
- Infinite-dimensional dynamical systems in mechanics and physics.
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- High-order discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
- DGM: a deep learning algorithm for solving partial differential equations
- Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
- A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
- Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
- A modified batch intrinsic plasticity method for pre-training the random coefficients of extreme learning machines
- When and why PINNs fail to train: a neural tangent kernel perspective
- Meta-learning PINN loss functions
- Error estimates for deep learning methods in fluid dynamics
- Numerical approximation of partial differential equations by a variable projection method with artificial neural networks
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines
- Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
- Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- MgNet: a unified framework of multigrid and convolutional neural network
- Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
- Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
- Greedy training algorithms for neural networks and applications to PDEs
- Classical Global Solutions for Non-linear Klein-Gordon-Schrödinger Equations
- Normal forms and quadratic nonlinear Klein-Gordon equations
- Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences
- Deep Neural Network Approximation Theory
- 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
- When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
- Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
- VAE-KRnet and Its Applications to Variational Bayes
- Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- Deep Learning Architectures
- Estimates on the generalization error of physics-informed neural networks for approximating PDEs
- A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions
- On the approximation of functions by tanh neural networks
- Higher-order error estimates for physics-informed neural networks approximating the primitive equations
This page was built for publication: Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms